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COP^-RIGHT DEPOSm 



MECHANICAL 

LABORATORY METHODS 

THE TESTLNG OF INSTRUMENTS AND MACHINES 

IX THE 

MECHANICAL ENGINEERING LABORATORY 

.\XD IX 

PRACTICE 

BY 

JULIAX C. SMALL WOOD, M.E. 

Fdlow, Johns Hopkiris University, and Sometime Associite Professor 

of Experimental Engineering, Syracuse University; Member 

American Society of Mechanical Engineers 

11 A ILLUSTRATIONS 



SECOND EDITION 
IlEYISED AXD ENLARGED 




NEW YORK 

D. VAN NOSTRAXD COMPANY 

25 Park Place 

1918 



r 






-■ v^ 



Copyright, 1914, 1918 

BY 

D. VAN NOSTRAND COMPANY 



« • • 



^Pff -3 IBIB 
PRICE, S.......^lQO_ NET. 



PRESS OF 

BRAUNWORTH & CO. 

BOOK MANUFACTURERS 

BROOKLYN. N. Y. 



Y ^C{.A4U44()8 



n^i^ I 



PREFACE TO THE SECOND EDITION 



This work has been enlarged and modified according to the 
requirements indicated by its use. The section dealing with in- 
struments contains a number of subjects not covered before, 
notably on recorders. The treatment of valve setting and steam 
engine testing is enlarged and improved. Under the heading of 
steam auxiliaries, the testing of condensers and feed water heaters 
is described. A new section is added on the testing of refrigerat- 
ing machinery, ammonia absorption and compression systems. 
Among the other newly included tests is one for the horse-power 
output of electric motors, which, it is believed, will be found of 
convenience in connection with the testing of motor-driven me- 
chanical units. In all there are described twelve additional tests. 

Sufficient tabular matter is appended in this edition to enable the 
user to calculate all the results sought by the various tests. This 
includes tables of the properties of steam and ammonia, a MoUier 
diagram, tables of areas of circles in three figures for cyHnder cal- 
culations, etc., four place logarithms, densities of water, and a sec- 
tion on hygrometry, together with all explanations necessary. 

All old and new numerical data and answers to problems have 
been thoroughly checked, and mistakes thus found corrected. 

The author wishes to express his obKgation to the various 
users of the first edition who have suggested improvements and 
additions. Such suggestions have been considered almost exclu- 
sively in the work of revision. It is modestly believed, therefore, 
that the book is materially bettered through this cooperation. 

Julian C. Small wood. 
Johns Hopkins University, January, 1918. 

iii 



r 



PREFACE TO THE FIRST EDITION 



In considering how best to describe what this book is intended 
to be, the author finds thoughts uppermost of what it is intended 
not to be. He has undertaken a subject already treated by a 
few admirable texts because there appeared in his own teaching 
the need of a brief work on the broad principles of experimental 
apparatus and methods. Therefore this book does not contain 
lengthy and detailed descriptions, nor does it attempt to cover 
all the instruments or methods of any class so that the student 
will understand them in all their details before commencing his 
work in the laboratory. 

It is obvious that the average student can learn details of 
instruments and apparatus much more readily by actual examina- 
tion of them than he can from printed and pictured descriptions. 
He should, of course, know the principles and purposes before- 
hand; then any deficiency of information may be made good by 
maker's pamphlets or by personal instruction in the laboratory. 

In dealing with any class of instruments, therefore, the text 
of this .book explains the principles of that class, or a subdivision 
of it, so that a brief explanation covers any specific instrument. 
Illustrations to help such explanations are diagrammatic, and not 
detailed drawings, the purpose being to make a simple pre- 
sentation. 

Instructions on how to operate engines, boilers, etc., have 
been omitted. The practicing engineer, presumably, does not 
need them. The student rarely memorizes them from a book, 
but he does grasp and remember them if imparted at the time 



^'1 



PREFACE 



when they may be associated wath the practice. It is believed 
that it is essential in any case to give such instructions per- 
sonally in the laborator3\ 

The principles of all except a few types of engines, descrip- 
tions of engines of differing types, and topics such as thermo- 
dynamics, etc., have not been included. It is assumed that the 
reader knows how the usual engines work before he is required 
to test them; at all events, if he does not, there are many texts 
open to him on these subjects. Ordinarily the college student 
of mechanical engineering has received a working knowledge 
of them from his other courses. This book is therefore on the 
subject of testing exclusively. 

The standards of the codes of the A.S.M.E. have been 
adopted in almost all instances, even where the author preferred 
other standards, for the sake of uniformity. The codes have 
not been quoted at length, however, because, in the first place, 
they are accessible to anyone, and secondh', their numerous 
items and many different expressions for practically the same 
results confuse, rather than help, the student. 

The value of such a book as this is intended to be depends 
largely upon the clarity of its presentation. The author has 
had exceptional opportunities in this particular, through nu- 
merous rearrangements of the subjects dealt with; the object 
being always to make them most easily understood by the 
student. 

The two main divisions deal with the testing of instruments 
and of machines, respectively. The first of these is subdivided 
so as to deal sc^parately with a group of instruments of a single 
type for a given purpose. Under each sub-division the prin- 
ciples of the instruments considered are first related, and then 
are given the methods of testing them. A number of problems 
are included, by the working of which the student may famil- 
iarize himself with the principles of the instrument before experi- 
menting with it. 



PREFACE vii 

The main division dealing with the testing of machines 
is similar in treatment; the principles introducing each sub- 
division in this case applying to the quantities usually sought 
in a test of the machine considered. 

The table of contents may be used as a synopsis of experi-' 
ments which may be referred to for the quantities to be meas- 
ured in the test of a given instrument or machine. 

A number of the testing methods described have not appeared 
elsewhere in book form. For some, the author is indebted to 
his former association with the University of Pennsylvania; for 
example, the method of setting the slide valve by the Bilgram 
diagram, the application of the method of least squares to indi- 
cator spring calibration, etc. Other of the methods, the author 
has developed at Syracuse University; notably those of testing 
indicator drum motion and reducing wheels. A number of 
original formulas are presented for the simplification of calcu- 
lations from test data. Upon such depend the methods given 
for testing gas engines and producers. Among others may 
be mentioned the formulas for the products of combustion of 
fuels, those for simplifying indicated horse-power determinations, 
etc. The sections dealing with these subjects, in somewhat 
different form, have been previously published in Power. 
Thanks are due to its editor, Mr. Fred. R. Low, for his courtesy 
in allowing their use here. 

To proportion such a work as this aims to be is difficult. One 
cannot help but be influenced by his personal inclinations toward 
one branch or another. Further, the field is too vast for one 
man to have covered thoroughly in all its branches through per- 
sonal experience. In view of these facts, the author states, in 
conclusion, that he would appreciate information concerning 
errors or defects from any who may use the book. 

Julian C. Smallwood. 
Syracuse University, January, 1914. 



r 



CONTENTS 



INTRODUCTION 
The Principles of Experimental Measurements 

PAGE 

ClassevS of errors. Limitations of instruments. Standards. Measure- 
ment of compound and variable quantities. Combining discordant 
observations. Rules for testing > . 1 

PART I. THE TESTING OF INSTRUMENTS 

Weights and Forces 12 

1. Calibration of Platform Scales. Principles, (a) Sensitiveness of 
scales. (6) Beam calibration, (c) Determination of leverage 
ratio, (d) Poise weight calibration, (e) Beam calibration by test 

of rider 13 

2. Evaluation of a Spring. Principles, (a) Spring scale by graphic 

method, (h) Spring scale by method of least squares 18 

Pressure 22 

3. Calibration of a Bourdon Gage. Principles, (a) Determination 
of the constants of the dead weight apparatus, (b) Calibration, 
(c) Adjustment of the scale, (d) Calibration of a recording pressure 
gage : . . . 23 

4. Calibration of a Draft Gage. Principles, (a) CaHbration by cal- 
culation. (6) Calibration by comparison 27 

ix 



X CONTEXTS 



PAGE 



Angular Velocity 29 

5. Calibration of a Tachometer. Principles and i}^es. (a) Calibra- 
tion against a continuous counter, (b) Calibration against a chro- 
nograph, (c) Cahbration of a recording tachometer 31 

Power 33 

6. The Constants of Friction Brakes. Principles, (a) Determination 
of the unbalanced weight, three methods, (b) Determination of 
the horse-power per pound thrust per revolution 34 

7. Cahbration of a Fan Brake. Principles, (a) Calibration against 
a transmission dynamometer, (b) Against a cahbrated motor, (c) 
Use of the horse-power constant 3>^ 

8. Calibration of a Transmission Dynamometer (Weight-arm Type). 
Principles, (a) Determination of constants. (6) Torque calibration 
by calculation, (c) Allowance for friction, etc. (d) Cahbration 

by comparison with prony brake 40 

9. Calibration of Transmission Dynamometer (Spring Type). 
Principles, (a) Static cahbration. (b) Allowance for friction, 
windage, etc. (c) Cahbration by comparison with prony brake. ... 45 



The Engine Indicator — Reducing Motions 50 

10. Calibration of the Indicator Spring and Pencil Motion. Principles. 

(a) Parallelism of the motion. (6) Ascending, descending, and 
combined spring scales by graphic method. (c) By method 
of least squares, (d) Methods of applying cahbration results to 
correct indicator diagrams, (e) Sampling 52 

11. Testing the Motion of the Indicator Drum. Principles, (a) Deter- 

mination of spring tension. (b) Of drum friction, (c) Testing 
indicator cord, (d) Adjustment of drum spring from overtravel. 
(e) Testing dram motion with motion tester. (/) Correction of 
diagrams from motion tester records 57 

12. Testing of Reducing Motions (Link Type). Principles, (a) Deter- 

mination of errors by line diagram, (b) By direct measurement. 64 



CONTENTS xi 

PAGE 

13. Testing of Reducing Wheels. Principles, (a) Determination of 

spring tension and of friction. (6) Determination of errors by the 
drum tester, (c) Correction of diagrams 67 

Irregular Areas and Mean Heights 76 

14. The Polar Planimeter. Principles, (a) Determination of the zero 

circle, two methods. (6) Comparison of direct readings with 
known areas, fixed center within and without the areas, (c) 
Comparison of readings to scale with known areas, (d) Arm 
adjustment to a required scale 76 

15. The Coffin Planimeter. Principles, (a) Comparison of records 

with known mean heights 85 

16. Averaging Circular Charts, (a) The radial planimeter. (h) Approx- 
imate average with polar planimeter 88 

Fluid Velocities — Meters 91 

17. Calibration of a Volume Water Meter. Principles, (a) Calibration 
against caHbrated scales or tank, (h) Correction factors 92 

18. Calibration of a Volimie Gas Meter. Principles, (a) Calibration 
with air measured by displacement. (6) Correction factors 93 

19. Weir Calibration. Principles, (a) Determination of the zero of 

the hook gage, (b) Of quantity rates and corresponding heads. 

(c) Of the coefficient of discharge at various rates 96 

20. Calibration of a V-notch Recorder, (a) Zero level of weir. (6) Cali- 
bration, (c) Sensitiveness 101 

21. Calibration of Nozzles. Principles, (a) Determination of quan- 
tity rates at different heads, (b) Coefficient of discharge 104 

22. Calibration of a Venturi Meter (Water). Principles, (a) Deter- 
mination of quantity rates at various pressure differences, (b) 

Of coefficient of discharge 107 

23. Calibration of a Venturi Meter (Gas). Same as 22 Ill 

24. Calibration of a Pitot Tube for Water. Principles, (a) Determi- 
nation of velocities and quantity rates by traversing, (b) Location 

of the point of mean velocity 112 



xii CONTENTS 

PAGE 

25. Calibration of a Pitot Tube for Gas. Principles, etc., same as 24. . . 115 

26. Calibration of an Orifice for Water. Principles, (a) Determination 

of quantity rate at various heads, (h) Of coefficients 119 

27. Calibration of an Orifice for Gas. Principles, etc., same as 26 121 

28. Calibration of an Anemometer. Principles, (a) Calibration against 
velocity in still air. (b) Curve of correction factors 124 

29. Test of a Calorimetric Apparatus for Measuring Gas. Principles. 

(a) Examination of instruments. (6) Determination of radiation 125 

30. Calibration of a Steam Meter. Principles and types, (a) Cali- 
bration by weighing condensate, (b) Sensitiveness of recording 
meters 127 



Thermometry , 131 

31. Calibration of High Reading Thermometers and Pyrometers. 

Principles and types, (a) Calibration against a standard. (6) Cal- 
ibration against steam temperatures, (c) Calibration against melt- 
ing and boiling points, (d) Stem corrections 133 



Heat of Steam — Calorimetry — Sampling 139 

32. The Throttling Calorimeter. Principles, (a) Determination of radi- 

ation correction 145 

33. The Separating Calorimeter. Principles, (a) Calibration of the 

dry steam meter. (6) CaUbration of the water gage, (c) Radiation 
correction 148 

34. The Condensing Calorimeter. Principles, (a) Determination of 

the water equivalent, {b) Of radiation correction 151 



Friction 154 

35. Oil Testers. Principles and types, (a) Determination of con- 
stants f 156 

36. Belt Testers. Principles, (a) Determination of constants 158 



CONTEXTS xiii 

PART 2. THE ANALYSIS OF COMBUSTION 

PAGE 

The Constituents of Fuels 163 

37. The Proximate Analysis of Coal. Sampling, (a) Determination 
of moisture, volatile matter, fixed carbon, and ash. (b) Estimation 

of total carbon and hydrogen 165 

The Heat Value of Fuels 170 

38. Determination of the Heat Value of Coal. Principles, Sampling. 

Determination by coal calorimeter. (6) By calculation from 
analysis 172 

39. Determination of the Heat Value of Gas and Oil Fuels. Principles. 

Samphng. (a) Higher heat value by Junker calorimeter, (b) 
Lower heat value, (c) Calculation of heat values of gas fuel from 
its analysis 177 

The Products of Combustion 180 

40. Exhaust Gas Analysis. Principles. CO2 recorders. Peagents. 

Sampling, (a) Determination of CO2, O2, CO, and N2. Precautions 

in operating. (6) Calculations from the analysis 189 

PART 3. THE TESTING OF P0\\:ER PLANT UNITS 

Steam Engine Testing 

41. Determination of Cylinder Clearance. Principles, (a) Linear and 

volumetric clearance by Hnear measurements. (6) Volumetiic 
clearance by water measurement, (c) Volumetric clearance of a 
gas engine from indicator diagrams 205 

42. Valve Setting of a Simple Slide Valve Engine. Principles, (a) 

Measurement of lead, (b) Setting for equal leads, (c) For equal 
cut-offs by the Bilgram diagram, (d) By the indicator, (e) Study 
of steam distribution by Bilgram or Zeaner diagrams 210 

43. Setting of a Corliss Valve Gear. Principles, (a) Adjustment of 
laps and leads. (6) Adjustment of goy.ernor rods, (c) Of dash-pot 
rod. (d) Checking by indicator 220 



xiv CONTENTS 

PAGE 

44. Mechanical Efficiency Test of a Steam Engine. Principles, (a) 
DeterminatioQ of ths indicated horse-power at various values 
of the brake horse-power. (6) Of the friction horse-power, (c) 

Of efficiency, (d) Of speed regulation 223 

45. Economy Test of a Steam Engine. Principles. Duration, (a) Steam 

consumption from the indicator diagram, by condenser, by steam 
meter, or by feed water measurement. Willan's Line. (6) CyHnder 
condensation, (c) Thermal efficiencies, British standard and Clausius 227 

46. Test of a Multiple Expansion Engine. Principles, (a) I.h.p., 
B.h.p., F.h.p., and mechanical efficiency. (6) Steam consumption, 
(c) Thermal efficiency, (d) Equivalent and aggregate IVI.e.p. (e) 
Steam accounted for by indicator diagrams. (/) Combined diagram 

(g) Ratio of Expansion, (/i) Diagram factor 236 

47. Economy Test of a Steam Turbine. Principles, (a) Determina- 

tion of useful horse-power. (6) Steam consumption, per horse- 
power- or kilowatt-hour. Willan's Line, (c) Thermal efficiencies, 
British standard and Clausius. (d) Separation of losses 242 

48. Economy Test of a Steam Power Plant. Principles, (a) Steam 
and heat consumption of engine and auxiliaries. (6) Heat added 
to feed water, (c) Heat lost to leakage and drips, (d) Heat 
balance 246 

Steam Pump Testing 

49. Valve Setting of a Duplex Steam Pimip. Principles, (a) Adjustment 

of lost motion of valve, (b) Readjustment after trial 250 

50. Mechanical Efficiency Test of a Reciprocating Steam Pump. Prin- 

ciples, (a.) Determination of indicated horse-power at various 
values of water horse-power, (b) Of mechanical and fluid losses. 
(r) Of efficiency. ((/) Of slip, (e) Of capacity 252 

51. Economy Test of a Steam Pump. Principles, (a) Steam con- 
sumption. (6) Thermal efficiency, (c) Duty 256 

52. Economy Test of an Injector. Principles. Selection of the inde- 

l)ondcnt variable, (a) Determination of the ratio of water pumped 
to steam used, (b) Of steam consumption, (c) Of efficiency, (rf) 
Of duty, (e) Of capacity 257 

53. Economy Test of a Pulsometer. Principles, etc., same as 52 202 



CONTENTS XV 

Boiler Testing 

PAGE 

54. Test of a Steam Boiler. Principles. Duration. Starting and Stop- 

ping. Sampling, (a) Determination of total coal and refuse. (6) 
Of total water evaporated, (c) Quantities to be found prior to 
calculations of results, (d) Determination of equivalent evapora- 
tion, per pound of coal, etc. (e) Over-all efficiency. (/) Heat lost 
to carbon wasted in refuse, (g) To dry exhaust gases, (h) To water 
vapor in the exhaust, (i) To incomplete combustion, (j) To 

radiation, (k) Other results, efficiencies, horse-power, etc 262 

• 

Testing Steam Auxiliaries 

55. Test of a Surface Condenser. Principles, (a) Ideal and actual 

vacuums. (6) Rate of heat transmission, (c) Effectiveness of 
heat transmission, (d) Weight of condensing water per pound of 
condensate 276 

56. Test of a Jet Condenser. Principles, (a) Ideal and actual vacuums. 

(b) Rate of heat transmission, (c) Weight of condensing water 
per pound of condensate 280 

57. Test of a Feed-water Heater. Principles, (a) Useful heat trans- 
mitted. (6) Effectiveness of heat transmission, (c) Available heat. 281 



Gas Engine Testing 

58. Testing the Adjustment of an Internal Combustion Engine. Prin- 

ciples, (a) Timing the valves. (6) Timing the ignition. (c) 
Adjustment of fuel mixture, (d) Adjustment of carburetors, (e) 
Test of timing by indicator 282 

59. Mechanical Efficiency Test of a Gas Engine. Principles, (a) 
Determination of indicated horse-power at various values of brake 
horse-power. (6) Of friction horse-power, (c) Of efficiency, (d) 

Of speed regulation 288 

60. Economy Test of a Gas Engine. Principles. Sampling. Dura- 

tion, (a) Fuel consumption. (6) Heat supphed. (c) Heat con- 
verted into useful work, (d) Heat lost to mechanical friction, (e) 



xvi CONTENTS 

PAGE 

To jacket water. (/) Determination of the volume of dry exhaust 
gas per cubic foot of fuel, (g) Heat lost to dry exhaust gas. (h) 
To water vapor in exhaust, (i) To incomplete combustion. (J) To 
radiation, (k) Determination of ratio of air to fuel gas 290 

61. Economy Test of an Automobile Engine. Principles, (a) Deter- 
mination of torque and brake horse-power at different speeds, (h) 

Of fuel consumption 300 

62. Test of a Gas Producer. Principles. Starting and stopping. 

Duration. SampHng. (a) Quantities to be found prior to calcula- 
tion of results. (6) Useful heat in the cool gas. (c) Sensible heat in 
the dry gas. (d) Heat lost to excess steam, (e) Heat transferred 
to scrubber water. (/) Heat lost to carbon in ash. (g) To radia- 
tion, etc. (h) Other efficiencies and results 302 



Testing Refrigeration Machinery 

63. Test of a Refrigeration Plant. (Ammonia Compression.) Principles, 
and definitions, (a) Refrigerating effect by measurement of the 
brine, (b) By ammonia measurements, (c) By approximate cal- 
culation, (d) Ice-melting capacity, (e) Coefficient of performance, 
actual. (/) Ideal, (g) Gallons of cooling water per minute per ton. 

(Ji) Overall economy 313 

64. Test of a Refrigeration Plant. (Ammonia Absorption.) Principbs. 

(a) Refrigerating effect. (6) Ice-melting capacity, (c) Ideal co- 
efficient of performance, {d) Gallons of cooling water per minute 
per ton. {e) Steam consumed by the generator. (/) Steam used by 
ammonia and brine pumps, (g) Work of ammonia pump, (h) 
Weight of anhydrous NH3 circulated per minute, (i) Concen- 
tration and specific gravity of the aqua, (j) Calculation of aqua 

and anhydrous weights 321 

66. Heat Balance of a Refrigeration Plant. (Ammonia Absorption.) 
Principles, (a) Weight of weak aqua per pound of anhydrous. 
(6) Heat added to XH3 and aqua in generator, (c) Steam-heat quan- 
tities, (d) Heat transfers in absorber, (e) Heat removed by con- 
denser water 329 



CONTENTS xvii 

Testing of Air Machinery 

PAGE 

C6. Test of a Fan Blower. Principles. Selection of the independent 
variable, (a) Determination of the horse-power supphed. (6) Of 
capacity, (c) Of horse-power supphed per thousand cubic feet of 
free air per minute, (d) Of air horse-power, (e) Of mechanical 
efficiency 336 

67. Test of a Reciprocating Air Compressor. Principles, (a) Deter- 
mination of capacity. (6) Mechanical efficiency, (c) Volumetric 
efficiency, (d) Efficiency of compression, (e) Over-all efficiency. 
(/) Separation of losses, (g) Heat measurements 340 



Testing of Water Motors 

68. Test of a Hydraulic Turbine. Principles. Selection of the inde- 

pendent variable. (a) Determination of available horse-power. 

(b) Of hydraulic efficiency, (c) Of best operating speed 347 

69. Test of a Hydraulic Ram. Principles. Selection of the independent 

variable. (a) Determination of capacity. (h) Of efficiencies, 
Rankine's and D'Aubisson's. (c) Curves 350 



Miscellaneous Tests 

70. Test of a Centrifugal Pump. Principles. Selection of the inde- 

pendent variable, (a) Determination of capacity. (6) Of horse- 
power supphed. (c) Of water horse-power, (d) Of efficiency, (e) 
Curves 352 

71. Test of a ** Power " Pump. Principles, (a) Water horse-power. 

(b) Available horse-power, (c) Mechanical and fluid losses and 
efficiencies, {d) Slip and capacity 356 

72. Test of a Hoist. Principles. (a) Determination of the ideal 

mechanical advantage, (b) Of the actual mechanical advantage at 
various loads, (c) Of corresponding efficiencies 358 

73. Tests of Lubricating Oils. Principles. (a) Determination of 
specific gravity. (6) Of viscosity, (c) Of flash, burning, and chill 
points. (cZ) Of the coefficient of friction, (e) Endurance tests 358 



xviii CONTENTS 

PAGE 

74. Horse-power Test of an Electric Motor. Principles, (a) Determi- 
nation of horse-power output. (6) Of efficiency 362 



APPENDIX 

Logarithms, Diameters and Areas of Circles, Densities of 
Water, Steam-vajoor Tension Tables, Properties of Steam, 
Tables and Diagram, M oilier Diagram, Properties of 
Ammonia, Hygrometry 365 

Reports of Engineering Tests 384 

A Method of Conducting Students' Tests 388 



I 
L 



MECHANICAL LABORATORY METHODS 



INTRODUCTION 

THE PRINCIPLES OF EXPERIMENTAL 
MEASUREMENTS 

The science of experimental engineering rests primarily 
upon the art of measurement. Conclusions relating to general 
laws or specific operating conditions, formed from test results, 
stand or fall according to the accuracy of measurement. 

Absolute Accuracy. There is no such thing as absolute 
accuracy of measurement except by accident. For instance, the 
length of a bar, measured with a scale graduated to one-hun- 
dredths of an inch, may appear to be 3 ins. By chance, it may 
be that the bar is 3 ins. long exactly, neither more nor less by an 
infinitesimal fraction. This, however, is very improbable. A 
micrometer may show it to be 3.005 ins. long. An instrument 
of still nicer capability might yield another decimal place, and 
so on. Thus, absolute accuracy presupposes an instrument 
with graduations corresponding to infinitely small fractions of 
a unit. 

Assuming that this condition could be sensibly complied 
with, it would still be necessary to prove the correctness of the 
instrument within its own graduations, and this could only be 
done by comparison with absolute standard lengths, that is, 
material objects known to have definite linear dimensions. 
But this implies measurement by an absolutely accurate instru- 



2 PRINCIPLES OF MEASUREMENTS 

ment. Thus, to create such an instrument, it is necessary to 
have the very article desired. 

Accidental Errors. Aside from instrumental limitations, 
accidental causes of error are a sufficient bar to absolute accuracy. 
Accidental errors are all those that cannot be eliminated by instru- 
mental or other corrections. They are due entirely to chance 
and are not s^^stematic except according to the law of probability 
and chance. Such errors are incurred in the calipering of a bar, 
for example, when the calipers are held on a slant instead of on 
a true diameter, when the calipers are held with var^dng degrees 
of pressure, when temperature changes momentarily affect the 
instrument, and so forth. 

Accidental errors are equally likely to be positive or negative 
from which it follows that in a series of observations upon the 
same quantity the probabilities are that the errors of excess 
will equal those of deficienc3\ 

Personal Errors. There is another class of errors knoTMi as 
*' personal errors ^' whereby a particular observer, by reason of 
his character, habitually reads too high or too low. This error 
may be estimated scientifically, the result being what is known 
as the '^ personal equation.'' Generally, in mechanical experi- 
mentation, this quantity is not an important one, being small 
in comparison with the usually unavoidable errors. 

We have, then, to consider two classes of errors which are 
bars to absolute accuracy in an}' measurement, namely, instru- 
mental and accidental. From an engineering standpoint, how- 
ever, absolute accuracy is neither necessary nor desirable, for it 
would be too laborious and cumbersome. It is not worth while 
to produce a result with ten or twenty significant figures when 
three or four are enough for practical requirements. Only that 
degree of accuracy is sought which accords with the dictates of 
common sense. 

Per Cent of Error. When a result is represented by three 
significant figures the error occurring through the omission of 



PRINCIPLES OF MEASUREMENTS 3 

the fourth Is less than one half of one per cent. Thus, the quan- 
tities 1010, 101.0, etc., may be correctly expressed 1015, 101.5, 
etc., but in each case the error is less than 5 parts in 1000 or 
one half of one per cent. With the higher digits the per cent 
error is correspondingly less, as when 999.0 is used for 999.5, 
the error then being about 0.05 per cent. In most cases we 
cannot secure results with less than 1 per cent of error, so that 
three significant figures are ample for their presentation. In many 
cases even less accuracy than this is consistent with the object 
or the conditions of the test. 

The Precision and Accuracy of Instruments should be examined 
before using them for experimental measurements. Precision 
has reference to the fineness of graduations, accuracy to their 
correctness. The value of the smallest graduation of an instru- 
ment is called its '^ least count.'' Suppose, as an illustration, we 
wished to weigh separately a number of objects of approximately 
100 lbs. so as to secure less than 1 per cent of error, that is, 
an error of less than 1 lb. A scales with a least count of 2 lbs., 
would do since a half a graduation could be estimated by eye 
with less probable error than 1 lb. A scales of any less precision 
however, would not be adequate. 

Standards. The accuracy of an instrument is established 
only by comparison with some ^^ standard unit,'' itself a copy, 
or a copy of a copy, of the ^' primary standard " kept at Wash- 
ington. The details of this sort of testing are given in Part I, 
but it is well to emphasize here that the necessary closeness of 
the approximation of any standard used to the primary standard 
depends entirely upon the least count of the instrument to be 
tested. Generally the standard is sufficiently accurate if it 
is correct within one quarter of this least count, and, if the standard 
is an instrument, its least count need not be less than one-half 
that of the instrument tested. It is thus seen that the word 
standard must be accepted with a relative sense, and that for 
engineering purposes secondary standards may be improvised 



4 PRINCIPLES OF MEASUREMENTS 

which are just as useful as the most accurate standard 
obtainable. 

Assuming instrumental co: ectness as great as consistent 
with the least count, there are two ways of securing greater 
accuracy of measured results: first, by using an instrument of 
finer graduations, and second, by making numerous repetitions 
of the measurement. When the latter is done a result with less 
probable error is obtained from the average of the observations 
than from any one of them. This is because by so doing 
the accidental errors previously mentioned are to some extent 
eliminated. 

Intrinsic Evidence of Accuracy. In experimental engineer- 
ing one of the greatest aids to accuracy is repetition. It is only 
by repeated trials that accurate conclusions can be framed because, 
not only are there variations due to erroneous measurement, 
but the quantities measured are generally variable ones, them- 
selves subject to chance. Under such circumstances, a single 
determination proves nothing and indicates little. On the 
other hand a series of determinations not only reduces the prob- 
able error of the result, but furnishes intrinsic evidence of its 
value. Consider, for example, a series of four measurements 
made upon a single constant quantity by an observer, A. These 
are 103, 98, 101, 98, the average of which is 100. Assuming 100 
to be the correct result (it is the best obtainable consistent with 
the observations, although, of course, not correct) then the 
error of each observation is the difference between it and the mean, 
or +3, —2, +1, —2, the plus and minus signs indicating whether 
the errors make the individual determinations greater or less 
than the mean. Now% If another observer measures the same 
quantity with the results 101, 100, 102, 101, averaging 101, 
the errors of his determinations will be 0, —1, +1, 0. It would 
be concluded at once that B^s measurements and result of 101 
were more accurate than A's because his errors, figured from the 
mean, are less than A's. 



PRINCIPLES OF MEASUREMENTS 6 

Compound Quantities. Most engineering measurements are 
upon compound quantities, the components of which are variable. 
The following parallel illustrates this case and also the graphic 
method later to be described. Fig. 1 represents the floor of a. 
room; and the solid diagonal line, the path of a ball that rolls 
across it. It is desired to locate as exactly as may be the path 
as it is traversed by the ball. The only exact data we have 
are that it is a straight line and starts at 0. At a given instant, 
one observer measures the distance of the ball from the wall 
OX and another from OY. These distances, x and y, are suf- 
ficient to locate one of the posi- 
tions of the ball and therefore 
its path, provided they are 
accurately determined. Acci- 
dental errors prevent this, how- 
ever, so that the path is falsely 
located on the line Oa. Obvi- 
ously, if a number of points^ 
instead of only one, could be 
located, a better result would 
ensue. 6, c, and d are such 



Acival Pafh-^. 







points. It is then found that Fig. 1. 

these points do not lie on the 

same straight line, the distances from the true path being 
the errors of their determinations. The question now arises 
how should these discordant observations be made to agree upon 
one result, which, though perhaps not the true one, is in best 
accord with the data. It is possible to locate a different line with 
each pair of observations, x-^y locating one, xi-^yij another, 
and so on. One might conclude that the average value oi x-iry 
would be best, but it can be shown by the theory of errors that 
the arithmetical mean does not yield the best result upon 
indirectly determined quantities. In this case, the result is 
obtained by measuring two other quantities; the determination 



6 



PRINCIPLES OF MEASUREMENTS 



is therefore indirect. The best result (referred to generally as 
*' most probable '') is a line so located that the sum of the 
squares of the distances from it of the points a, 6, c, and d shall 
be a minimum. Such a line can be determined mathematically, 
but it is generally drawn by eye judgment. 

Variables, Independent and Dependent. A large part of 
mechanical experimentation is parallel to this simple illustration. 
Two variables, bound together by a more or less rigid law, are 
measured, and from the result the law is deduced. The law is 
not always represented by a straight line, but often by a 
curve. Whichever it is, it is the business of experimentation 
to find. 

One of the variables can always be controlled; the other 
then follows it according to the law binding them. For example, 
w^hen a spring is extended by a force, there are two quantities, 
namely, the force and the extension, which combined give the 
law of the spring. In their measurement we may add predeter- 
mined increments of weight and let the extension vary as it may, 
or we may add weight enough to cause predetermined increments 

of extension and let the weight 



yV 



c 







/ 




•J 




y« 







I <0 

rorce. Poundi 
Fig. 2. 



15 



lbs. applied to a spring and 1 



increase as it may. The pre- 
determined quantity is called 
the ^^independent variable"; 
the other, '' dependent.'' 

It is almost always desirable 
to present such measurements 
as points and to locate by them 
a smooth curve. This is done 
by adopting a pair of rectangu- 
lar axes, OX and OY and scaling 
them according to the units 
measured. In Fig. 2, for instance, 
1 in. along OX represents 10 
in. along OY represents \ in. of 



PRINCIPLES OF MEASUREMENTS 7 

spring extension. The observations 7.5 lbs. and 0.375 in. are 
thus shown by the point indicated, and so on. 

In many cases there are three variables, as the pressure, 
temperature and volume of a gas. It is then customary to keep 
one of them constant throughout a test, arbitrarily control another, 
constituting the independent variable, and let the third vary as 
it may. 

If the relation between the variables appears to be satisfied 
by some other curve than a straight line, such a one is drawn. 

Intrinsic Evidence of Accuracy. If any point of a plotted 
series lies markedly off the line, it may be concluded logically 
that its determination contained some large error, or mistake, 
and it may be thrown out of consideration entirely. Similarly, 
the value of a set of measurements may be judged by the closeness 
of the plotted results to a smooth curve. 

It will be readily seen that the value of graphic presentation 
of results lies in the fact that their relative variation is visuaUzed 
and can therefore be grasped by the mind much more easily 
than could mere columns of figures. 

Conventions for Plotting. The independent variable, as a 
matter of convention, is plotted horizontally, the other vertically. 
Exceptions to this rule are calibration curves and stress-strain 
diagrams of materials; the one having instrument readings, 
the other, deformations, plotted as abscissas. 

Compound Variable Quantities. In the case of the spring 
the two variables, when combined, give a constant quantity, 
namely, the number of pounds per inch of extension. It is not 
often that the required compound quantity is a constant one, 
although it is sought to keep it so throughout one set of measure- 
ments. As an example, the mechanical efficiency of a steam 
engine depends upon the amount of work it is doing; the greater 
its output, within its capacity, the greater its efficiency. Sup- 
pose it is desired to measure the efficiency at a given output. 
The engine is operated to deliver this horse-power, no more and 



8 PRINCIPLES OF MEASUREMENTS 

no less. But, owing to variations in steam pressure, governor 
action, and the like, it is possible to keep the horse-power out- 
put only approximately constant; it fluctuates somewhat through 
accidental causes more or less outside our control. Further, 
even if it were possible to keep it constant, the internal friction 
of the engine varies and this causes the ^vork done in the cylinder 
to vary. Consequently, the efTiciency, which is the delivered 
horse-power divided by the power developed in the cylinder, 
will vary. So aside from variations in the results produced by 
unavoidable errors of measurement, there are accidental varia- 
tions in the true value of the result, even when all the controllable 
conditions are kept as constant as possible. It is hke measuring 
the height of a small spot of light which persists in fluctuating 
up and down through a limited space. Clearly, a single measure- 
ment w^ould be altogether insufflcient, for it might represent a 
high or a low value, even if accurately made. Obviously, the 
best that can be done is to keep controllable conditions as con- 
stant as possible w^hile taking not one but a number of measure- 
ments. It may now be understood how such conditions will 
determine the precision necessary, because of the uncertainty 
of the true value of the result. 

Rules for Testing. The following rules should be observed 
when measuring variable compound quantities. 

First, For one value of the independent variable, the series 
of measurements made of each separate quantity may be averaged. 
All such averages may be used in a single calculation of the desired 
result. 

Second, Observations of fluctuating quantities should be 
made at equal time intervals to secure a true average. 

Third. The number of observations necessary of any quan- 
tity depends upon the constancy of the quantity. 

Fourth, Tests of time rates should cover a sufficient duration 
of time to reduce the error of initial and final measurements to 
1 per cent of the total quantity. 



PRINCIPLES OF MEASUREMENTS 9 

Fifth. In time rate tests, intermediate time readings should 
be taken to check rate constancy. 

Constancy of Conditions. Referring to the third rule, if 
all the conditions of a test could be kept absolutely constant, 
only two sets of readings would be necessary. The two would 
give identical results; the second would be made only to check 
the accuracy of measurement of the first. In some cases this 
condition is approximated, as, for instance, electric motor 
driven blowers. In other cases some of the quantities fluctuate 
more than the rest; under these circumstances the time interval 
between measurements of these quantities should be smaller 
than for the others, so that there may be more values obtained 
for them. 

Duration of Time Rate Tests. The fourth rule may be 
illustrated as follows. In measuring the pounds of water per 
minute flowing into a tank, the cross-section of the tank is 
measured, and the difference of water in it before and after an 
observed time interval is figured by noting the corresponding 
difference of the water levels. The water level is measured 
with a scale graduated to tenths of an inch. With such a scale, 
it is possible to make an error of gV in. (half a division) at each 
measurement, totaling iV in. It would be necessary, then, 
to make the duration of test long enough that yV in. be 1 per cent 
of the total rise in water level, that is, long enough for the w^ater 
to rise 0.1 in. -r- 1.0 per cent = 10 ins. This calculation allows 
for the maximum error probable, but it is on the safe side. 

Intermediate Readings. The table of observations on p. 10 
illustrates the fifth rule. If the column of differences shows 
approximately equal values corresponding to equal time inter- 
vals, the result is valid. Any marked departure from constancy 
should throw suspicion upon the result. If the readings at 3:00 
and 3:10 only had been taken, we should be ignorant as to rate 
constancy. As has been pointed out, the reliability of the result 
depends upon constancy of conditions. 



10 PRixciPLES OF ^^EAsrRE^rE:xTs 

Time Height DifFerences 
3:00 5.0 in 

0.95 in. 
3K)2 5.95.. 

1.05 
S.-Oi 7.00 

1.05 

Sm 8.05 

1.00 
3.-08 9.05 

1.05 
3:10 10.10.. 

A further advantage from intermediate readings is that they 
strengthen the determination against mistakes. This was shown 
in the illustration of the path of the ball. From the obsenations 
just cited, the result ordinarily would be figured thus 

f 10.1 -5.0) X area ,• • u 

77- — : = cubic mches per mm. 

10 mm. 

which is the same as though no intermediate readings had been 
taken. If, however, a mistake in measurement were incurred 
in the first or the last reading, as 6.0 instead of 5.0 ins., or 20.1 
instead of 10.1 in^^., this mistake would not be apparent, and 
the result misleading or worthless. Intermediate readings would 
disclose such a mistake, and the set of observations involved 
could be discarded without sacrificing the others. 

Id time quantity measurements it is always best to record 
the time of day instead of time interv'als merely. This insures a 
correct record of the time. Otherwise it is easy to note an interval 
such as three minutes when two or four actually have elapsed. 
A further advantage is that possible irregularities in results 
may then be accounted for by related happenings that might 
be associated only by a knowledge of the time of occurrence. 



PRINCIPLES OF MEASUREMENTS 11 

Before closing the general subject, it is well to emphasize 
the importance of figuring in the laboratory rough results 
from the observations as soon as obtained. This appHes to 
commercial as well as student work. By so doing, many faults 
in operation and in the appUcation of instruments may be detected 
and remedied in time. It is especially valuable to plot a curve 
of the variables as the test progresses, for it will reveal the accuracy 
or error of the determinations at the time when such knowledge 
is most valuable. 

Problem Ii. Temperatures of liquid in a pipe are read as follows: At 
11:00 A.M., 90°; at 11:05, 100°; 11:15, 100°; 11:20, 90°. Compare the 
average of these four readings with the probable average if a reading had been 
taken at 11:10. Ans., 95°, 96°. 

Problem L. If the thermometer used in Problem li has a least count 
of 2°, what is the probable percentage of error in each reading? 

Ans., 1.1%, 1%. 

Problem I3. In a specific heat determination, two thermometers are 
used reading about 50° and 70°, respectively. What should be their least 
count that the probable error of the result be less than 2 per cent? 

Ajis.y 1°, or less. 

Problem I4. The rate of water flowing into a tank placed on a platform 
scales is to be determined by taking weighings and timing. If the rate is 
about 20 lbs. per minute and the probable error in reading the scales at 
starting and stopping is ±| lb., how long should the test be continued to 
secure less than 1 per cent of error? How many intermediate readings could 
be conveniently taken in this time? Arts., about 5 min. 



r 



PART ONE 

THE TESTING OF INSTRUMENTS 



WEIGHTS AND FORCES 

These are measured by comparison with known weights 
with the aid of a system of levers such as in a beam balance, 

or by reference to the amount they 

t „ deform some elastic object, as a spring, 

^ I =J which has been previously calibrated 

/\ against standard weights. When a 
^^-fe^^J-N leverage system is used so that a 
YiQ, 3. large force may be measured by com- 

parison with a small known weight, 
it is necessary to know the ratio of the lever arms. In Fig. 3, 
for instance, the force F is measured by the relation 

W = -F 
m 

71 

in which — may be referred to as the ^' leverage ratio/' 

The calibration of any force measuring appratus rests primarily 
upon the force of gravity as a standard. " Standard weight '' 
is a misnomer in that the weight of the body so called, being the 

12 



SCALES AND PRESSURE GAGES 



13 



force of gravity between it and the earth, actually varies with 
the locality of the body. Standard mass is a better term. A 
standard mass establishes a standard force when the accelera- 
tion of gravity at the given locality is known. 



1. Calibration of Platform Scales 

Principles. The platform scales Fig. 4^ is arranged so that 
a large weight, W to be measured, may be balanced by a small 



Bh. 




^ 



j< , a — >K-b-:4 

Inolicafes a Fulcrvm. 



w 



W 



i 



I 



>lc* < 



I 



1 



.i-^ J 



Fig. 4. — Platform Scales. 



weight on the beam, B. The small weight is either or both P 
on the poise or i?, the rider, acting at .a variable distance from the 
beam fulcrum. If P balances IF, then by the principle of moments, 



fxf=^=?4+f^7>^f 



w 



?^ 



14 SCALES AND PRESSURE GAGES 



It is arranged that - = -> X- so that 
^ c f c 

^ d ^^^ d 
b c 

W ac 
and ^T = r^ = the leverage ratio. 

/^ ba 



(a) The Sensitiveness of the Scales. This is determined by 
placing a large weight on the platform, weighing it, and then 
finding the smallest additional weight that will cause a deflec- 
tion of the beam which gan be nicely balanced by the rider. This 
additional weight is also a measure of the precision of the scales, 
provided the beam graduations are small enough to take cog- 
nizance of it. 

(b) Beam Calibration. Readings of the beam are taken 
corresponding to a number of standard weights. These should 
be sufficient to cover fairly the range of the beam. If standard 
weights of convenient size are not available, a number of small 
weights may be standardized for the purpose by using a calibrated 
scales with slightly greater precision than that of the scales to 
be tested. (See p. 3.) 

If the instrument readings do not agree with the true weights 
a calibration curve should be plotted, having the instrument 
readings as abscissas and the true weights as ordinates. This 
curve may be used to get corrected values at any part of the beam. 

(c) The Leverage Ratio may be found by measurement of 
the lever arms, but this method is difficult and subject to error. 
A better one consists of balancing a standard weight on the poise 
with a standard weight on the platform, then calculating the 
ratio of these weights. The nominal leverage ratio may be learned 
by examination of the poise weights. They are marked with 
their actual weights and the weights they are intended to balance, 
as, for instance, 1 Ib.-lOO lbs. This gives a nominal leverage 



1 SCALES AND PRESSURE GAGES 15 

ratio of 100. To test the accuracy of this, place, for example, 
a standard ^-Ib. weight on the poise and a standard 50-lb. weight 
on the platform. If they do not balance, add enough weight 
(shot is convenient) to either one or the other until a balance 
is secured. This additional weight may then be accurately 
measured and the true leverage ratio found. 

(d) Poise Weight Calibration. The indications of the poise 
weights are accurate if the leverage ratio is true and if the actual 
weights of the poise weights are as marked. They should there- 
fore be weighed by a calibrated scales of sufficient precision. 
It should be noted that any error in the poise weight is multiplied 
in the instrument reading by the leverage ratio. The standard 
scales should therefore weigh these weights to within an amount 
equal to the precision of the scales to be tested divided by its 
leverage ratio. 

If the actual weight of a poise weight is not as marked, or 
if the leverage ratio is not true, then the weight balanced on 
the platform is 

Actual weight of poise weight X actual leverage ratio 

instead of the amount indicated by the marking. For instance, 
if the poise weight intended to measure 100 lbs. actually weighs 
0.99 lb. instead of 1 lb., and if the leverage ratio is 99.5 instead of 
100, then the weight on the platform balanced by it is 0.99X99.5 = 
98.5 instead of 100 lbs. In this way the true weight balanced by 
each poise weight may be found. 

(e) Beam Calibration by Test of Rider. In some types of 
platform scales, there are no poise weights, a number of riders 
on different beams being used. In such cases, the following 
method may be used : 

The weighing beam to be tested is represented by Fig. 5. 
With no load, the rider is in the position shown, its pointer being 
at the zero graduation, and its beam floating. With a load W 
on the table, the rider must be moved through a distance d to 



16 SCALES AND PRESSURE GAGES 1 

secure balance. If the scales are correct, the weight of the rider 
must be such that the distance d will be that between the zero 
and the graduation marked W, Now, instead of using the rider, 
another weight could be applied at any convenient part of the 
beam as shown by S, of such amount as to secure a balance 
when the load W is on the table. Therefore, the moment of 
the weight S about the fulcrum / must equal the moment of 



r- ■i:::::::::tz^:::::- ^ 



d ^ 

*• 1 



®);^ h) ' I ' I ' I ' I ' I Ol ' !| ' I ' I 

■ »' I H I I 



t^ 



I * 



Fig. 5. 

the rider which is replaced. Letting R denote the weight of 
the rider, 

SXD=RXd 

Let the ratio of the load on the platform to the balancing 
weight S be L. Then 

W 

Substituting this in the first equation, and simplifying, we find 
the weight which the rider must have in order to suit the existing 
graduation of the beam : 

To apply this relation to the calibration, a value of W is 
chosen, and the distance between the beam graduation marked 
W and the zero graduation is carefully measured. This deter- 
mines W and d. A point is then chosen to represent 2), and 
its distance measured from the fulcrum /. To find the ratio 
L, it is not necessary to apply the full weight W to the platform. 



1 SCALES AND PRESSURE GAGES 17 

since the ratio W : aS is constant for all values of TT, the ratio 
of levers being established by the selection of D. Therefore 
the following procedure is used. An appreciable, but not in- 
convenient, number of weights is placed on the platform, these 
having been previously measured with a standard scales. They 
may consist of anything available that may be readily moved. 
A balance pan, improvised from paste-board and wire, is then 
attached to the beam at the distance D from the fulcrum, and 
to this pan are added shot or other small weights until a balance 
is secured. If desired, the weight of the pan may be previously 
balanced by the usual beam counterweight so that the experi- 
menter need deal with the added weight only. The latter should 
then be accurately weighed. This result, divided into the weight 
applied to the table, gives the desired ratio L. The value thus 
obtained completes the data necessary to calculate the weight 
of the rider according to the equation previously deduced. The 
rider is then removed from the beam and weighed; if the actual 
checks the calculated weight, the instrument is proved at the 
graduation marked W. Any other graduation may then be 
checked by proportion, since the distances of the graduations 
from the zero mark must vary directly with the indicated loads. 

Problem li. Five weights of about 10 lbs. each are to be standardized 
in order to calibrate a beam up to 50 lbs. How closely should these secondary 
standards be weighed, if the least count of the beam to be calibrated is 4 
oz.? (Note. Have regard for the cumulative error.) 

Problem I2. Referring to division (c), how closely should the shot be 
weighed for less than 1 per cent of error in the determination of the leverage 
ratio? 

Problem I3. The least count of a scales to be calibrated is 4 oz. Its 
leverage ratio is 100 : 1. How closely should the poise weights be weighed 
so that their calibration shall be within the precision of the beam? See {d). 

Problem I4. Prove that it makes no difference in the instrument indica- 
tions where W is placed on the platform. 

Problem I5. If the rider, R^ is too light, will the resulting error be con- 
stant at all indications of the beam or will it vary and why? Will the error 
be plus or minus? 

Problem le* If the poise is too light to bring the beam down with nothing 



18 SCALES AND PRESSURE GAGES 2 

on the platform, can a scales, otherwise accurate, be used for correct results 
^s-ithout pre\'ious calibration, and how? If too hea\'>'? 

Problem l;. Calculate the proper weight of the rider and check by 
weighing it. 

Problem li. Examine a scales to find if its leverage ratio may be ad- 
justed. 

2. Evaluation of a Spring 

Principles. In a large class of instruments, it is necessary 
to know the amount of force required to extend, compress, or 
tw-ist a spring per unit of deformation. This quantity is called 
the '' spring scale.'' According to Hooke's law, it is a constant 
\nthin the elastic limit of the material. In many cases the movable 
end of the spring is attached to bome combination of links and 
gears designed to indicate, magnify, or translate the motion. 
When the applied force is increasing, the friction of such links 
or gears makes the instrument read low, since the indicator is 
moving up the scale and friction tends to hold it back. With 
a decreasing force, the instrument reads high for a similar 
reason. Suppose an external force F is applied to a spring 
instrument, which is correct except for the effect of friction, 
first by increasing the external force to the value F, and then by 
decreasing it to this value. Then, if S is the spring scale, Ei and 
E2, the extensions in the two cases, and X the friction, 

F = SxEi+X 

Adding F = SXE2-X 

2F = S(Ei+E2) 

^ S(E,+E2) 
• ^ = 2 

That is, the effect of friction may be eliminated by taking increas- 
ing and decreasing readings at each load applied, dividing the 
sum of the extensions thus found by two, and using the result 
as the extension caused by the external force. 



SCALES AND PRESSURE GAGES 



19 



(a) Spring Scale by Graphic Method. Take as an example 
the following measurements of force and extension. 



Force 
lbs. 


Extensions 


Increasing 
In. 


Decreasing 
In. 


Average 
In. 


10 
20 
30 
40 
50 


0.32 
0.64 
1.02 
1.32 

1.68 


0.34 
0.70 
1.08 
1.36 
1.70 


0.33 
0.67 
1.05 
1.34 
1.69 



These are plotted as points on coordinating paper, and then 
is drawn what appears to the eye as the best straight hne to satisfy 
each of the three sets of points.* Fig. 6 shows the hne for the 
increasing readings; the other two curves are similar. When 
it is desired to apply a calibration only to increasing readings, 
the ascending line is used, and similarly wath the descending. 
The combined line gives the best results when the instrument 
is used for measurement of a fluctuating quantity. 

To figure one of the spring scales, as for instance the ascend- 
ing, the line for which is shown by Fig. 6, a point is selected 
near its extremity, asFi— i/i, this point not necessarily repre- 
senting a pair of observations. It should, however, lie on the 
line. Then the spring scale equals 

S (ascending) = 



El 



or, using numerical values, 



47.4 — 1.0 
= — T-n?: — = 29.0 lbs. per inch 



* Certain researches of the author indicate that the decreasing values of 
force and extension do not follow Hooke's law within appreciable amounts 
and that, theoretically, they must follow a curved line. (Physical Review, 
October, 1911.) To represent them by a straight line is therefore merely 
a convenient approximation. 



20 



SCALES AND PRESSURE GAGES 



to be used when the readings of the instrument increase; sim- 
ilarly with the other two spring scales. 

Note that the intercept, k, is taken into account. If the 
curve does not pass through the origin it is because of friction 
or backlash of the indicating mechanism or to a false zero reading 
of the extension. 



DU 








F,-47.4 


L 




/sS> 




40 

1" 
















/ 


/ 








/ 






15 






/ 






5 

£20 




/ 










/ 








to 


/ 


^ 








/ 












/ 











To 



a40 0.80 1.20 

Extension, in Inches 



IGO 



LOO 



Fig. 6. 



(b) Spring Scale by Method of Least Squares. The theory 
of errors shows that the most probable straight line to fit such 
data is one so located that the sum of the squares of the distances 
of the plotted points from the line shall be a minimum. This 
can be calculated as follows. The equation of the line may be 
written 



2 SCALES AND PRESSURE GAGES 21 

in which k and S are unknown, and F and E are represented 
by a number of more or less discordant observations. This 
equation may be multiphed through by the coefficient of each 
unknown, thus 

F=SE+k 

EF = SE^+Ek. 

In each equation the corresponding values of E and F are sub- 
stituted thus forming two series of equations. Each series is 
summed and the resulting equations are known as the " normal 
equations ^^ oi k and >S respectively. These may be solved as 
simultaneous equations to obtain the most probable value of S. 
Using the data of the ascending scale tabulated, 

F=ES+k EF=E^S-{-Ek 



10 = 0.32>S+/c 3.2=0.1024*S+0.32/c 

20=0.64>S+/c 12.8=0.4096aS+0.64A; 

30 = 1.02S^k 30.6 = 1.0404aS+1.02A: 

40 = 1.32iS+/c 52.8 = 1.7424aS+1.32/c 

50 = 1.68/S+/c 84.0 = 2.8224iS+1.68/c 



150 = 4. 98^+5/c 183.4 = 6.1172^+4.98/0 

Normal equation of k. Normal equation of S, 

From these, by eliminating fc, it is found that aS = 29.38 lbs. per 
inch. 

The descending scale is found similarly and the combined 
scale is obtained by adding the corresponding normal equations 
from the ascending and descending values. 

Note that the numerical values in the equations should be 
figured to four or five significant figures since, when the equa- 
tions are solved, the first two or three figures disappear by 
subtraction. Labor can be saved by using multiples of ten, 
or simple figures, for the independent variable F, and by using 
a pocket-book table of squares to obtain the values of E^. 

Problem 2i. Calculate the descending and combined scales for the 
example given by methods (a) and (b). Compare them. 



22 



SCALES AND PRESSURE GAGES 



Problem 22. Prove from the fact that the area under each curve equals 
work done that the descending curve cannot be a straight line. 

Problem 2^, From the ascending data of the example given, figure and 
compare the different results for the ascending spring scale obtained by the 
following (faulty) methods. 50^-1.68. The average of all the F's-^ average 
of £"s. The average of F-^E, The average of each increment of F-j- cor- 
responding increment of extension. The average increment of F divided by 
average increment of E, 

PRESSURE 



The measurement of pressure is a special case of force measure- 
ment, wherein the area over which the force is distributed is taken 
into account. Pressure is a compound unit being the number 
of units of force per unit area. 

In cahbrating pressure measuring devices, the standard 
force is that of gravity acting on some standard mass. 

Pressure is usually expressed in pounds per square inch. 
Its measurement is always relative, that is, based upon some 
other pressure as a datum. A pressure gage reads so man}- units 
above atmospheric pressure, for instance, and a vacuum gage, 
so many below. Absolute pressure, or pressure counted from 
zero, is an abstract conception and cannot be measured directly 
by instruments. 



Wt--a0561 Lb. 

Area'1 Sc[. In. 

Pr.^a036tLh 
pcrScf.In. 



Fig. 7 



wt^o. 

Area' 
Pk' 0.0561 



^ 



0722 Lb. 
2 Sq. In. 
LtxpcrScf-fn. 



Wt'a0722LtA 

AreO'tSo/Jn 



Pr.-a0722Lb 
perSq. In. 



2" ->^ 

Fig. 8. 
Pressure Produced by Water. 



Fig. 9. 



>•' 



Another measure of pressure is the height of water or other 
liquid which by its weight balances the pressure to be measured. 



•=C\ 



i 






3 SCALES AND PRESSURE GAGES 23 

Fig. 7 represents a cubic inch of water. At 60° F., this weighs 
0.0361 lb. Since the area this force acts upon is one square 
inch, the pressure produced is 0.0361 lb. per square inch. Two 
cubic inches of water, arranged as in Fig. 8, would have twice 
the weight, but it would be imposed upon twice the area; hence 
the pressure would be the same. Arranged as in Fig. 9, however, 
the area would be one square inch, and therefore the pressure 
would be twice that shown by Fig. 7. It follows that the pres- 
sure produced by a given mass of water varies directly with its 
height and is independent of its cross-section. 
Hence, inches or feet of water may be regarded 
as units of pressure. 

Fig. 10 shows the application of this prin- ^ ^YJ 
ciple in the ^^ manometer. ^^ The pressure in 
the chamber C is said to be ^' X inches of 
water ^^ and this equals 0.0361 XX lbs. per square 
inch. The absolute pressure in C equals this Fig. 10. 

quantity plus the pressure of the atmosphere Manometer, 
represented by the arrow at A . 

Mercury is also used in manometers, and since its specific 
gravity is about 13.6 at 60° F., the equivalent is 

1 in. of mercury = 0.0361 X 13.6 = 0.49 lbs. per square inch. 

3. Calibration of a Bourdon Gage 

Principles. The Bourdon gage consists essentially of a hollow 
circular spring which is deformed when subjected to internal 
fluid pressure, the deformation causing a pointer to rotate upon 
a graduated dial. (See Fig. 11.) The pointer is readily removed 
so that it can be set at any part of the dial to correspond to an 
applied known pressure. 

It should be noted that the deformation of the hollow tube 
is proportional not to the absolute pressure within the tube, 
but to the difference of pressure within and without. The Bourdon 
pressure gage, therefore, always indicates pressures above at- 



24 



SCALES AND PRESSURE GAGES 




SECTION 
OF TUBE 

Fig. 11 



■Mechanism of Bourdon 
Gage. 



mosphere, since the outer surface of the tube is subjected to 
atmospheric pressure; and to convert its readings into absolute 
pressures, one must add the baro- 
metric pressure expressed in the 
same units. 

The vacuum gage works on the 
same principle as the one just de- 
scribed, the only difference being 
that the excess of pressure is on 
the outside of the tube (Fig. 11) 
causing a contraction of the coil, 
instead of an expansion, which is 
indicated, generally, in inches of 
mercury less than the barometric. 

The testing apparatus consists of a chamber in which any 
desired pressure may be obtained and to which is attached some 
accurate device for measuring it. The pressure is generally 
obtained by some simple form of hand pump. The measuring 
device is either a ^^ test gage,'^ a column of mercury, or a set of 
weights acting on a plunger of known area arranged to produce 
the pressure desired. The test gage is not a desirable standard 
as it needs calibrating itself from time to time. The mercury 

column is a cumbersome and expensive 
apparatus for pressures above a few pounds, 
although it is the most accurate method of 
measuring the true pressure. Besides, a 
high degree of accuracy is not needed since 
the least count of commercial gages is 
generally not less than 5 lbs. It is neces- 
sary, however, to use the mercury column 
when testing vacuum gages, and con- 
venient since they are graduated in inches 
of mercury and not in pounds per square 




Fig. 12. — Vacuum 
Gage Tester. 



inch. (See Fig. 12.) The standard weight 



SCALES AND PRESSURE GAGES 



25 



method is convenient but the friction of the plunger prevents 
true records. Fig. 13 shows an apparatus of this type. 



Weicjfrh for 
J Measur'inq Pressure 






For Acijusfmenf\^ 




Fig. 13.— Dead Weight Gage Tester. 

(a) The Constants of the Standard Weight Apparatus are the 
area of the plunger and the actual weights of the test weights, 
from which may be figured the actual pressures produced by 
them. The area is measured by cahpering the plunger. The 
weights should be determined by comparison with standard 
weights with a degree of precision compatible with the least 
count of the gage to be tested. Note that the pressure produced 
by the plunger and attached pan is always applied. 

(b) Calibration. Set the pointer to read accurately at the 
division most used and then take a series of readings of true 
pressures and instrument readings increasing and decreasing, 
from which plot a calibration curve. Convenient procedure 
is as follows. With the weights appUed to produce the desired 



26 SCALES AND PRESSURE GAGES 3 

is as follows. With the weights apphed to produce the desired 
pressure, depress the plunger a trifle by hand and close the cock 
between the gage and the pressure chamber, thus confining 
in the gage a pressure slightly greater than produced by the 
weights. The pan and weights are now revolved to reduce 
friction at the plunger and the cock slowly opened. The pressure 
indicated by the gage will then slowly decrease and a reading 
may be taken. For increasing values, the pan is raised a trifle, 
otherwise the procedure is the same. The two readings thus 
found are added and divided by tw^o to ehminate the effect of 
friction. If the gage is to be used for ascending pressures, then 
the calibration resulting from them only should be used. Gen- 
eralh^ this is not the case and the calibration from the combined 
readings is preferable. 

(c) Adjustment of the Scale. When the calibration curve is 
plotted, if the instrument is in error, it will be noted that the 
indications either increase or decrease with relation to their 
true value. Inside of the gage will be found an adjustable link, 
by means of which the travel of the pointer may be made greater 
or smaller for a given motion of the tube. This link should 
be changed in length until a correct motion of the pointer on the 
scale is found, as proved by a calibration curve. 

(d) The calibration of a vacuum gage is essentiall}- the same 
as for a pressure gage, an air pump and mercury column being 
used instead of the apparatus described. 

(e) Calibration of a Recording Pressure Gage. The working 
principle of the usual pressure recorders is that of the Bourdon 
tube, the tube being helical in form instead of circular. This 
provides a sufficient motion to the free end of the tube, to which 
a pen arm is attached; and magnification by links is not needed. 
The pen arm swings over a circular chart which is uniformly 
rotated by clockwork. The curve traced by the pen is thus 
one of pressure shown radially against time circumferentially. 
(See Fig. 14.) 



SCALES AND PRESSURE GAGES 



27 



When calibrating, the clock should be stopped, and the instru- 
ment read the same as a simple indicating gage. The dead- 
weight apparatus may be used, the 
pen arm first being set to indicate 
accurately at the desired point on the 
chart scale. 

Recorders are often set at a con- 
siderable distance from the points at 
which the pressure is to be ascertained. 
If the gage is either above or below 
such a point, and the connecting tube 
is full of liquid (such as condensed 
steam when the gage is below a steam 
pipe whose pressure is sought) then a 
correction for the head of liquid must 
be applied. Since 2.3 feet head is 
equivalent to 1 pound per square inch, 
the correction for a difference of height of H feet is 

J7/2.3 lbs. per square inch, 

and this should be subtracted from the instrument indications 
when the gage is set below the point of measured pressure, and 
added when above. 

Problem 3i, If the table and plunger of the test apparatus weigh 15| oz., 
how much pressure does their weight produce in pounds per square inch, 
the diameter of the plunger being 0.50 inch? Is the difference between 
this and 5 lbs. per square inch worth considering? 

Problem 82. If the area of the plunger of the test apparatus is about 
\ square inch, how closely should the test weights be weighed to come within 
the precision of a gage having a least count of 5 lbs.? 




Fig. 14. — Mechanism of 
Pressure Rec:rder. 



4. Draft Gage Calibration 

Principles. Draft gages are generally special forms of manom- 
eters used to measure the reduced pressure (less than atmosphere) 
in chimne3^s, which creates the draft. This is expressed in inches 
of water and, as it is usually only a few tenths, the ordinary 




28 SCALES AND PRESSURE GAGES 4 

U-tube will not do. Fig. 15 shows a favored type. It is the ordi- 
nary manometer with one leg on a slant, so that the travel of the 
r-r _<---yn level of the liquid used is magnified. 

In use, the instrument should be set 
true to its designed level and the 
hquid adjusted so that the level in 
Fig. 15.— Draft Gage. the inclined tube standsat zero when 

there is no difference of pressure. 
Calibration of a draft gage can be made by examination of 
its graduations and the weight of the liquid, or by comparison 
with a standard instrument. 

(a) Calibration by Calculation. Having set the gage to its 
designed level, a horizontal line H-H^ is drawn wdth a spirit-level 
through the zero of the scale. The vertical distance T^ from the 
last graduation on the scale to this line is then measured. The 
level of the liquid in the inclined tube will fall this distance for 
the whole scale, but the level in the enlarged tube will rise an 
amount equal to the length S of the scale in inches multiplied 
by the ratio of the squares of the diameters of the bores of the 
small to the large tube. If water is the liquid, the sum of the 
rise and fall thus calculated equals the inches of water, pressure. 
The true pressure corresponding to any other graduation can 
now be found by proportion. 

The calculation of the rise of level in the enlarged tube assumes 
that the bores are uniform. 

Commercial forms of this i\\)Q of gage generally use oil 
for the liquid, having a definite specific gravity less than one. 
When such a gage is cahbrated, the total vertical difi"erence of 
level is found as before. The corresponding height of water is 
then found by dividing this by the specific gravity of the partic- 
ular liquid used. The specific gravity may be obtained by using 
a hydrometer or by weighing a known volume of the liquid. 

(b) Calibration against a Standard Gage. Connect the 
gage to be tested with a piece of rubber tubing to the standard 



SCALES AND PRESSURE GAGES 



29 



gage as in Fig. 16. The pressure in this tube may readily be 

reduced to any desired amount by applying the lips to the 

branch B, the pinch-cock serving 

to confine the suction when 

obtained. Enough readings for 

a calibration curve should be 

taken. 

For the standard gage, an 
impromptu instrument is easily 
made by using an inclined tube of 
generous length. 





Fig. 16. — Arrangement for Testing. 



Fig. 17.—Kent's Draft Gage. 



Problem 4i. If a draft gage using water at 70° F. is correct, calculate 
the rise in temperature that would produce 1 per cent of error. (See p. 
for weight of water.) Ans. 60°. 

Problem 42. In the type of gage shown by Fig. 17, the reduced pressure 
inside the inverted can M causes it to descend against the resistance of the 
spring (neglecting the buoyancy of the water). If the area of the inverted 
can is 50 square inches and if the pressure within is tu inch of water less 
than without, what is the total downward force on the can? How much 
will the spring extend because of this force if the spring scale is 0.2 lb. 
per inch? Ans., 0.9 in. 

Problem 43. Deduce an equation for the gage shown by Fig. 17, neglect- 
ing buoyance, to show the relation between the extension of the spring and 
the draft, lq inches of water, causing it. 



ANGULAR VELOCITY 

The units are usually whole revolutions per minute, abbreviated 
R.p.m. The simplest form of instrument to measure this quan- 
tity is the hand counter. This consists of a worm and wheel. 
The worm is part of a small spindle tipped with rubber so that, 



30 ANGULAR VELOCITY METERS 4 

if held against the end of a revolving shaft, it turns with the shaft, 
thus giving a circular motion to the worm wheel. The wheel 
is graduated so as to indicate the number of turns of the spindle. 
In operation, the hand counter is applied during a period of time 
measured with a watch, and from the readings of watch and coun- 
ter, the revolutions per minute of the shaft are calculated. 

The Continuous Counter, or cyclometer, is a variation of 
the hand counter in that its spindle is geared to a series of wheels 
with numbered faces, partially exposed, so as to show at any 
time the total number of revolutions. Some forms of continuous 
counter are driven by a reciprocating lever instead of a revolving 
spindle. In both forms, the instrument usually receives its 
motion from a small pin on the end of the shaft whose revolu- 
tions are to be measured, which pin acts as a crank. 

The Tachometer gives instantaneous indications of revolu- 
tions per minute without measuring time. The spindle trans- 
mitting the speed bears a pair of weights so linked that they move 
outward from the spindle by centrifugal force, and against the 
restraint of a spring. In so doing they actuate a pointer on an 
appropriately graduated dial. As the centrifugal force, and 
therefore the motion of the weights, are proportional to the speed, 
the pointer may register the speed instantaneously. 

On account of the variation in their internal friction and in 
the stiffness of their springs wdth use, tachometers should be 
calibrated before using on important work. 

Recording Tachometers are made in a variety of forms, and, 
for the greater part, depend upon the action of centrifugal force 
on a solid or fluid mass. Thus, the simple tachometer just 
described may be made as a recorder if the centrifugal weights 
actuate a pen arm (instead of a dial pointer) which travels over 
a clock-work driven chart. An example of the centrifugal fluid 
tachometer is the Bristol. This consists of a small air blower 
which is driven by the shaft whose speed is to be found. The 
blower creates a partial vacuum which increases as the speed 




5 ANGULAR VELOCITY METERS 31 

increases, and vice versa. The vacuum is transmitted to and 
recorded by a pressure recorder, the chart of which is graduated 
in revolutions per minute. Still another recording tachometer 
consists of a small generator, driven by the shaft considered, whose 
speed variations are evidenced by the generator voltage. This 
is recorded in terms of revolutions per minute upon a time chart. 

The Chronograph is an instrument by which a graphic record 
of time is made. Fig. 18 shows a form. Paper is caused to roll 
over a drum, D, by clockwork, and in 
contact with the paper is a pen on a 
light arm, A, which is caused to vibrate 
at regular time intervals by connection, 
electrical or otherwise, with a standard 
clock. Another arm, A\ is similarly 
actuated by connection with the shaft ^^^' 18.— Chronograph, 
the speed of which is to be measured, 

so that it vibrates once each revolution. Thus, there are drawn 
two lines, one broken at intervals representing time, the other, 
revolutions; from which may be obtained angular velocity. 

The Tachagraph is a very sensitive tachometer, arranged to 
give an autographic diagram of angular velocity. It is used to 
measure minute changes of speed within a revolution, 

5. Calibration of a Tachometer 

Principles. The standard should be either a continuous 
counter or a chronograph. In either case it is necessary to have 
a revolving shaft of variable and controllable speed to cover the 
whole range of operation of the tachometer. A small steam 
engine of variable speed may be used, or a water wheel, or a 
series wound electric motor. A shunt woimd motor will do if a 
rheostat is put in series with its armature circuit. A small water 
rheostat is convenient as it giver a wide range of resistance. 

(a) Calibration against a Continuous Counter. Increasing 
and decreasing readings of the tachometer should be taken at 



32 ANGULAR VELOCITY METERS 5 

each speed. The mean of these readings is plotted against the 
speed as shown by the counter for the cahbration curve. 

If the continuous counter is arranged on the variable speed 
shaft so that it can be applied at the same time as the tachometer, 
the procedure is as follows. Starting with a slightly lower speed 
than is required, the tachometer is connected and the speed raised 
to the desired amount. Time and counter readings are then 
taken wth the tachometer still connected. If the speed remains 
constant as indicated by the tachometer, the observations are 
valid after the second readings of time and counter are taken. 
The decreasing readings are o])tained similarly. 

When the speed is high the counter becomes difficult to read. 
This may be obviated by an arrangement for throwing the counter 
in or out of connection with the variable speed shaft. 

A hand counter may be used if it can be applied to one end 
of the shaft while the tachometer is at the other. It is inadvisable 
to take readings of the two instruments at other than the same 
time as the speed may vary. 

The time during which the revolutions are counted should 
be of sufficient length to reduce the error of starting and stopping 
to less than the precision of the tachometer. For instance, if 
the tachometer cannot be read closer than 5 R.p.m., at any 
part of its scale, then at 250 R.p.m. the error in reading the in- 
strument is 2 per cent, and the error in reading the time should 
l:>e made less than this, say 1 per cent. Now a moving number 
is unlikely to be timed with an ordinary watch closer than one- 
half second; therefore the counting should proceed through at 
least 50 seconds to get the desired precision. Similarly, at 500 
R.p.m., the error in reading the instrument is 1 per cent; the 
starting and stopping error should be reduced to ^ per cent, and 
the timing should proceed through 100 seconds. The use of a 
stop-watch will greatly reduce this time, as it reduces the starting 
and stopping error to one-tenth of a second or less. 

(b) Calibration against a Chronograph. With this apparatus 
the tachometer may be left in connection with the variable speed 



5 ANGULAR VELOCITY METERS 33 

shaft, and the speed first increased and then decreased in a series 
of steps at constant speed. The moving record may be stopped 
while the speed is being adjusted. The time for counting may be 
very much reduced, as the chronograph shows the whole number 
and fraction of turns of the shaft that occur during a time beat 
which may be as small as desired. 

(c) Calibration of a Recording Tachometer. The principles 
to be observed are exactly the same as given under (a) and (b). 
It should be observed that certain types of this instrument have 
a time lag in their indications behind the true R.p.m. of shaft 
whose speed it is intended to measure. That is, when this shaft 
changes in speed, a certain interval is required before the change 
is felt at the recorder. This interval should be noted and reported. 

Problem 5i. Using an ordinary watch, how long should a continuous 
counter be timed when calibrating a tachometer witl a range from 600 to 
1200 R.p.m., at the even hundreds, if the least count is 10 R.p.m.? How 
long, if a stop-watch is used? 

POWER 

Power is defined as the time rate of work. Quantitatively, 
w^ork is the product of a force and the distance through which 
it acts, the unit being foot-pounds. A horse-power is defined as 
33,000 foot-pounds of work done in one minute. If an engine 
can deliver 33,000 foot-pounds of 
work in one minute it is rated as 
1 horse-power; if 66,000, 2 horse- 
power; and so on. 

Generally engines deliver a rota- 
tive effort. Suppose, for example, 
that an engine transmits an average Fig. 19. 

tangential force of F pounds at its 

crank pin. (See Fig. 19.) In one revolution, this force will act 
through a distance equal to the circle through which the crank 
pin has passed, or 27rr, r being the radius of the crank in feet. 




34 dyna]mo:meters 6 

The foot-pounds of work per revolution are then 2-rXFy and if 
there are N revolutions per minute, the work done per minute 
will be 27rrFxX, and the horse-power will be 

2xrFAr 

33,000* 

The quantity rF is called the '' torque/' 

Dynamometers are used for measuring power. Generallj^ the 
speed is measured independently of the dynamometer bj' a hand 
counter or otherv\'ise, so the dj^namometer is apphed only to 
measure the torque. This is done by balancing the torque by a 
measured force acting at a kno^Ti distance from the center of 
rotation. 

There are two broad classes of d^mamometers: absorption 
by w^hich the power to be measured is converted into some form 
in which it cannot be used; and transmission j by which the power 
is passed on unchanged. 

6. Constants of Friction Brakes 

Principles. Friction brakes ma}^ be used as absorption 
dynamometers, and of these the Prony brake is the commonest 
and most accurate form. (See Fig. 20.) It consists of a band 
wrapped around a pulley on the shaft whose power is to be 
measured, so arranged that by tightening a hand wheel, H, the 
friction between the wheel and band can be controlled. The 
band is held from turning by means of an arm, A, attached 
to it, and supported by some force measuring device at its free 
end. Considering the friction between the band and wheel as 
a single force,/, then the horse-power developed is 27rr7.Y-^ 33,000; 
r' being the radius of the wheel in feet. Now since the force 
W exerted by the scales, S, produces equihbrium, by the prin- 
ciple of moments 

RW = r% . 



DYNAMOMETERS 



35 



and therefore by substituting in the expression for horse-power 
just given 

33,000 

In practice, if the force, TF, and the revolutions per minute, Ny 
are measured, the horse-power may be calculated, the length of 
the arm being known. B is called the '^ brake constant/' 




Fig. 20.— Prony Brake. 



It should be noted that the arm, A, by its weight produces 
a force acting on the scales which should not be included in the 
force balancing the frictional effort. This should be allowed 
for by determining the ^^ unbalanced weight '' of the brake, or 
" brake zero,'' and subtracting it from the scale readings. 
Methods of determining the brake zero will be given later. 

The rope brake is a modified form of prony brake. Fig. 21 
shows such a one, the friction between the rope and the wheel 
being balanced by the force of the scales on the right less the 
weight on the left. The difference between these quantities is 



/ 36 



DYXAMOMETERS 



the value of W in the formula, and the value of R is the radius 
of the wheel plus the radius of the rope. There is no unbalanced 

weight if the lengths of rope on each 
side of the pulley are equal. The 
friction, and therefore the horse- 
power, ma}' be varied by increasing 
the weight on the left or by taking 
more turns of the rope about the 
wheel; either procedure greatly in- 
creases the friction. 

Fig. 22 gives two other arrangements 

of rope brake and their equations. 

In operation, the heat generated by the friction is removed 

by circulating water within the brake wheel, the latter being 

provided vdth. internal flanges for that purpose. It is generally 




7J^7m777777777777?77^77777Tr77777T7p77 

Fig. 21. — Rope Brake. 




^///■V'-." 



w///////////////////////////////// 



Torque = (5 -Brake Zqxo)R Torque = (TF->S-w;)i2 
Fig. 22.— Rope Brakes. 



suflBcient to feed the water at a rate just equal to the loss by 
steaming. 

Hydraulic friction brakes are the same as those just described 
in principle though quite different in detail. A series of discs 
mounted on the power shaft revolve in a casing filled with water 
under pressure, the casing being free to revolve about the shaft. 
The friction between the discs and the water causes a turning 



6 DYNAMOMETERS 37 

effort upon the casing which is balanced by a force measuring 
device the same as with the common prony brake. Regulation 
is secured by varying the water pressure. The constants are the 
same as for the other types, but in most cases there is no unbal- 
anced weight. 

(a) Determination of Unbalanced Weight. If friction could 
be entirely eliminated between the band and 13 y wheel, the unbal- 
anced weight would be the reading of the scale, Fig. 20. But, 
no matter how loose the band is, there is always some friction 
between it and the wheel tending to hold up the brake arm when 
the wheel is stationary. If the brake is removed from the wheel 
and supported by a knife edge or circular pin at the point k, 
Fig. 20, the other end being supported by the scales as in opera- 
tion, then the scales will indicate the unbalanced weight pro- 
vided that the flexible band does not change in its weight dis- 
tribution. This is one method of finding this quantity. 

Another method consists in revolving the brake wheel first in 
one direction and then in the other, and noting the corresponding 
readings of the brake scales. With the wheel revolving clockwise, 
Fig. 20, the scales will indicate the unbalanced weight plus the 
force necessary to balance the friction at the band. Anti-clock- 
wise, it indicates the unbalanced weight minus this force, since 
the friction is reversed. Calling the force balancing friction X, 

Unbalanced Wt.+^ = lst reading 
Unbalanced Wt. — X = 2d reading 

Adding, Unbalanced Wt. = (lst+2d reading) -^2. 

When applying this method it is necessary that X remain con- 
(Btant. The band should be quite loose, the bearing blocks 
wet with oil, and the wheel turned at a uniform rate. 

The third method is the same in principle as the second, 
but the brake is revolved instead of the wheel. The spring 
balance. Fig. 20, is first drawn upward giving the weight +X 
reading; then the weight of the brake is allowed to draw it 



38 DYXAMOMETERS 6 

dowTi for the weight —X reading. Note that if the spring 
balance is slanted out of its correct position relative to the brake, 
a component force will be indicated. 

(b) Determination of the Horse-power per Pound of Thrust 
per Revolution. This is the '' brake constant " or 2-i?-=- 33,000. 
R should be measured with a tape or measuring rod. Note 
that R is the perpendicular distance from the center of the brake- 
wheel to the Une of the balancing force TF, Fig. 20. 

Problem 6i. \Miat is the brake constant ii R = 5 ft. 3 J in.? If unbal- 
anced weight of the brake is 2.5 lbs., what scale reacUng would be necessary 
to balance 40 H.P. at 160 R.p.m.? Aws., .001; 252.5 lbs. 

Problem 6^. By the third method, the scales indicate 10 lbs. when the 
brake is pulled up. (Fig. 20.) Its weight is not enough for it to drop, con- 
sequently the balance is reversed and the brake pulled down, for the weight 
— X reading. The scales then indicate 2 lbs. What is the unbalanced 
weight? Ans., 4 lbs. 

Problem 63. If the unbalanced weight is 5 lbs., where should weight be 
added to balance the brake, and how much? 

Problem 64. Given an arrangement like Fig. 20 except that the wheel 
turns anti-clockwise and the spring balance is inverted. If the R.p.m. = 100, 
arm = 4 ft., unbalanced weight = 14 lbs., and the balance reads 20 lbs., what 
is the horse-power? Ans., 2.59 H.P. 



7. Calibratiox of a Fan Brake 

Principles. Fan brakes are convenient for measuring the 
output of high speed motors that operate at variable speed, 
such as automobile engines. Fig. 23 shows such a one. The 
energy of the shaft is absorbed by imparting kinetic energy and 
heat to the air. With a fixed set of vanes the power thus absorbed 
varies as the cube of the speed. The capacity of the brake at a 
given speed of rotation can be changed in only two ways, namely, 
by changing the size of the vanes or their distance from the cen- 
ter of the shaft. The first method may be taken by swinging 
the vanes around on their arms so that the effective area resist- 



DYNAMOMETERS 



39 







O 
O 

o 
o 
o 



o 
o 
o 
o 






]> 









Fig. 23.~Fan Brake. 



ing motion is lessened. For the second method, the fastenings 
of the vanes to the arms may permit the desired radial variation. 
This type of dynamometer is sometimes mounted on a frame 
independent of the engine shaft and driven by a belt. In this 
case, the belt losses and brake journal 
friction (more or less iiideterminate quan- 
tities) are added to the resisting effort. 

(a) Calibration against a Transmission 
D3mamometer. By means of a transmission 
dynamometer, simultaneous values of torque 
necessary to drive the fan and revolutions 
per minute are determined for a given 
adjustment of the vanes. From these 
values, the horse-power absorbed at each 
speed may be calculated, and a curve of 
horse-power vs. revolutions per minute plotted. This curve 
may be used for finding the horse-power, when the brake is in 
usual operation, from readings of the rotative speed. 

(b) Calibration against a Calibrated Motor. If the fan brake 
is belt driven, it may be run by a variable speed electric motor, 
through the same belt and pulleys to be used when the fan measures 
power. At a definite speed of the fan, readings of the armature 
and field currents of the motor and of its speed are taken. The 
belt is then removed, a prony brake applied to the motor pulley, 
and the horse-power of the motor measured under the same 
conditions of current and speed. If all controllable conditions 
are the same, this horse-power will be the same as that absorbed 
by the fan at the applied speed. A series of similar trials at 
different speeds will give data for a calibration curve. 

This calibration will be somewhat in error owing to the fact 
that the reaction on the motor bearing caused by the prony brake 
thrust is somewhat different from the reaction due to the belt 
pull; hence the friction of the motor under the two loads will be 
slightly different. 



.^ 



40 DYNAMOMETERS 7 

(c) Use of the Horse-power Constant. The power absorbed 
by the fan for a given setting of tlie vanes equals 

KX density of the airX(R.p.m.)''^ 

in which i? is a quantity very nearly constant. Assuming that 
the density of the air also is nearly constant, the product of K 
and the density may be found experimentally at a convenient 
speed. Then the horse-power at any other speed may be found, 
approximately, by multiplying this product by the cube of the 
speed. 

The experimental determination of K times air density is 
made by taking readings according to either method (a) or (6). 
Then the desired value equals the horse-power divided by the 
cube of the apphed speed. 

Variations in belt losses and in the value of K make this 
method inexact. 

Problem 7i. WTiat percentage of error will be caused by the density 
of the air changing from that corresponding to a barometer of 29.5 in. of 
mercury, at which the fan is calibrated, to 30 in.? What percentage by a 
change of temperature from 60 to 80° F.? Atis., 1.6%; 3.8%. 

8. Calibration of a Transmission Dynamometer, 
Weight-arm Type 

Principles. The weight-arm type of transmission dj^namora- 
eter consists of some device by which the torque of a revolving 
shaft can be balanced by a standard weight or weights acting 
with a known leverage. The balancing torque caused by the 
weights is thus a measure of the horse-power when the revolutions 
per minute are known. There are many forms of this type of 
d}Tiamometer differing mainly in mechanical details. 

Belt dynamometers of different kinds are in the weight-arm 
class, of which Fig. 24 represents one. The torque of the trans- 



DYNAMOMETERS 



41 



mission shaft is equal to the effective^belt pull, T1-T2, multipHed 
by the radius at which it acts, r. Disregarding the friction at 
the bearings of the pulleys, p and p', the reactions at these 
bearings will be 2Ti and 27^2, respectively, as will be seen from a 
consideration of the belt forces. Taking moments about the 
fulcrum /, and disregarding the weight of the arm A, we have 

WR +2T2a =2Tia 
from which 

Ti- T2 =WR-^2a 
and the torque 

= r{Ti -T2)=rWR-^2a. 






^'Transmission 
Shaft 



]' P/aiform \ 
Scales 

Fig. 24. — Belt Dynamometer. Fig. 25. — Pillow Block Dynamometer. 

Thus by balancing the belt torque by a known weight W, the 
power may be measured if R/a is known and if a suitable allow- 
ance is made for friction. 

A pillow block dynamometer is shown by Fig. 25, consisting 
of three gear wheels the middle one of which is mounted on a 
pillow block, so as to bear freely on a weighing device. The 
turning force of the driver, F, produces an equal resisting force 
at the gear on the transmission shaft, barring friction. The 
reaction W, which can be weighed by the scales, thus equals 
2Fj and hence the torque of the transmission shaft is 

W 
Fr^^Xr. 



42 



DYNAMOMETERS 



8 



The reaction W may also be measured by hanging the middle 
wheel from one arm of a lever above the other carr>dng a balanc- 
ing weight. 

Some forms of pulley block dynamometer omit the middle 
wheel and weigh the reaction of the bearing on the transmission 
shaft directl3\ When this is done, the transmission shaft must be 
arranged to rest freely on the weighing de\dce. 

The Webber differential dynamometer is a variation of Fig. 
25, but similar in principle. It is shown diagrammatically by 
Fig. 26, which represents three bevel gears, the middle one being 




Fig. 26. — Webber Dynamometer. 



supported by a lever whose fulcrum lies on the common axis 
of the driver and transmission shafts, Similar to the principle 
showTi by Fig. 25 the net force on the middle gear is 2F, This 
is balanced by the dead weight T7 acting with a lever arm of R 
feet. Taking moments of the forces acting on the lever around 
its fulcrum, we have 

2Ft = WR 

from which, torque transmitted = 

Fr=ffl. 



As actually constructed there is another gear on the lever-arm, 
as indicated by the dotted line. This does not change the 
relation, merely substituting for the moment 2Ft two moments, 



8 DYNAMOMETERS 43 

Fr+Fr. Also there is a jockey weight on the arm in addition 
to the pan weights similar to the arrangement of a platform 
scales. 

The Emerson power scale is a dynamometer by which the 
torque is passed to a transmission pulley on the driver shaft 
through a lever system so arranged that a thrust in an axial 
direction is given to a non-revolving sleeve on the shaft. This 
thrust is balanced by dead weights which consequently measure 
the torque. 

Friction of the moving parts of the dynamometer itself has 
not been accounted for in the equations. Generally the dyna- 
mometer indicates the torque necessary to overcome its own 
f ricton ' and windage in addition to the external torque on the 
transmission pulley which alone it is the purpose to measure. 

(a) The Constants of a Djrnamometer of the Weight-arm 
Type are first, the true values of the dynamometer weights; 
second, the unbalanced weight of the arm or lever system; and 
third, the leverage ratio produced by the arm or lever system. 

The true values of the weights should be determined with a 
scales sufiiciently precise to keep within a reasonable percentage 
of error. 

The unbalanced weight of the arm may be found as for a 
prony brake, by revolving the driver shaft in first one direction 
and then the other by hand, and noting the resulting force at the 
end of the arm where the weights are to be applied. A spring 
balance may be used for this purpose. Half the sum of the two 
readings equals the unbalanced weight. 

The ratio of levers may be obtained generally by direct 
measurement. In the case of the Webber dynamometer, for 
instance, only the length of R, Fig. 26, is necessary. For the 
arrangement of Fig. 24, the ratio is R a, as shown by the equation. 

(b) Calibration by Calculation. The torque equivalent to 
each dynamometer weight acting at the previously determined 
leverage is found by multiplying its value in pounds by the lever- 



44 



DYNAMOMETERS 



8 



age ratio as shown In the equation for the dj^namometer in ques- 
tion. A series of such determinations furnishes data by which 
the horse-power corresponding to any weight may be found 
when the d\'namometer is in usual operation. 

The torque equivalent to the unbalanced weight of the arm 
should be added to that indicated b}^ the weights applied if the 
turning effort of the driver on the arm is upward. If it is down- 
ward, the power being then gaged by scales instead of weights 
simpl}^, the torque equivalent to the unbalanced weight of the 
arm should be subtracted. 

(c) Allowance for Friction, Windage, and Centrifugal Force. 
To allow for friction, a crude but convenient approximation is 
based upon the assumption that the frictional resistance is the 
same under all conditions of external torque. If, then, the 
dynamometer is run with the transmission shaft entirely free, 
the weight to balance the arm gives the correction to be sub- 
tracted from the readings in usual operation. Windage is 
included in this, but if the dynamometer is to be used at various 
speeds, similar corrections should be determined at these speeds 
to allow for the varying value of the windage. 

With some dynamometers having revolving levers, bell- 
cranks, and the like, such as the Emerson power scale, centrifugal 

force acting on these .-parts may 
cause a distortion of the indica- 
tions. This is allowed for under 
the windage corrections. 

(d) Comparison with Prony 
Brake Measurements is the most 
valid means of calibrating any 
transmission dvnamometer. To 
do this, a prony brake is fitted 
to the transmission pulley and 
is adjusted so as to balance each 



K R---.-> 




^Ploi fe carry irtof pulleys, 
free to turn on center 



Fig. 27. — Belt Dynamometer. 
dynamometer weight in turn, power being delivered as in usual 



DYNAMOMETERS 45 

operation. The torque shown by the prony brake is the true 
torque measured by the corresponding weight. When a jocky 
w^eight is used as for the Webber dynamometer, a calibration 
curve of torque against jockey weight positions is convenient. 

If the dynamometer is to be used at various speeds, it should 
be calibrated at a number of them, the results to be in terms 
of either horse-power or torque, as shown by the brake, correspond- 
ing to each dynamometer weight. In this way friction, windage, 
and centrifugal force may be taken into account. 

Problem 81. Deduce the torque equation for Fig. 27. 



9. Caijbration of a Transmission Dynamometer, 

Spring Type 

Principles. Spring dynamometers differ from the weight- 
arm type in that the torque to be measured is balanced by a 
a spring or springs through which the torque is passed. The 
spring is consequentl}^ deformed by either a tensile, compressive, 
or twisting stress. If the constant of the spring is known (that 
is, the number of pound-feet of torque necessary to cause a unit 
deformation) then by noting the deformation, the horse-power 
may be determined. 

Fig. 28 shows, in part, the principle of the Van Winkle dyna- 
mometer. Power is taken off at the loose pulley P which is driven 
through springs by the disc attached to the driver shaft. The 
resulting deformation of the springs permits a change of position 
of the pulley relative to the disc, and this operates a bell-crank 
lever (not shown) which in turn actuates a pointer on a stantionary 
dial. The dial is arranged to indicate horse-power direct. 

Another spring dynamometer, made by the Central Laboratory 
Supply Company, is shown by Fig. 29. Two shafts are connected 
by a spring through which the power to be measured is passed. 
These shafts are provided with discs arranged as commutators. 



46 



DYNAMOMETERS 



being insulated from the shafts except at the shaded portions 
showTi under the brushes. In this position, an electric circuit is 



—Loose Trans, Pultetj 
•f/,<r--Oisc. Keyed 




Drlver6horff 




Fig. 28. — Van Winkle D\Tiamometer. 



[>river 




Fig. 29. — Central Laboratory D>Tiamometer. 

completed causing a click in a telephone receiver. The right-hand 
brush is stationary, but the one on the left is so arranged that it 
may be swung around the shaft. In operation, the latter is 



9 



DYNAMOMETERS 



47 



manipulated until a click is heard in the receiver, indicating that 
both contact pieces are passing under the brushes at the same 
time. Then the angular motion of the left-hand brush shown 
on the dial and measured from its clicking position when there 
is no torque delivered, is equal to the twist of the spring, and 
hence is a measure of the torque. 

In usual operation small variations of the torque, due to 
belt flapping, etc., make the clicking position somewhat variable. 
It is therefore convenient to read the maximum and minimum 
angles at which no click is heard and to take the average of these 
as the twist of the spring. 

The Flather dynamometer (Fig. 30) differs from the foregoing 
in that the torque is communicated to the transmission pulley 
through small pistons, p, working in cylinders filled with oil. 



^V//^Wy777j^ 



"Loose Trans. Pulley 



<— Arm, Keyed 





Fig. 30. — Flather Dynamometer. 



The fluid pressure* thus produced is transmitted through tubes, 
t, and a longitudinal hole through the center of the driver shaft. 
Connecting with this hole at the end of the shaft is an indicator 
by which a graphic record of the pressure is made. Since this 
pressure is proportional to the torque (being produced by the 
driving force at the cylinders, c, acting at a constant distance 
from the shaft center) it is a measure of the horse-power. 



48 DYNAMOMETERS 9 

Friction affects the indications of a spring dynamometer in 
two ways. First, since the friction of the loose transmission pulley 
or of the transmission shaft on its bearings always acts against 
the motion, it makes the indicated torque greater than the true 
external torque. Second, friction of the indicating mechanism 
makes the indications for increasing torques low, and for decreas- 
ing high, similar to the action of friction in a pressure gage. 
Generally the first effect is greater than the second. 

(a) Static Calibration. With the driver shaft clamped, the 
transmitting shaft may be twisted with a series of known weights 
acting at a measured distance from the center of the shaft. Thus 
a series of values of torque may be obtained with the correspond- 
ing instrument indications, the latter being either in dial gradua- 
tions, degrees of twist, or height of an autographic diagram, 
as may be appropriate to the instrument tested. To apply the 
static torque, the transmission pulley may be used as the arm, 
a rope being tied to a spoke and passed over the pulley face from 
which to hang the weights. If the necessary number or size 
of standard weights are not available; a lever may be clamped 
to the transmission shaft, and a single weight applied at various 
distances from the center. In this case, the moment of the lever 
should be accounted for. 

Increasing and decreasing values of the torque should be applied 
and corresponding readings taken to eliminate the effect of fric- 
tion. For the increasing readings, the weights are caused to 
bring up the torque gradually to the desired amount. For 
decreasing, extra torque is brought upon the shaft by bearing 
on the weights by hand; then gradually removing the hand pres- 
sure so that the torque will decrease to the desired value. The 
average of each pair of readings is then plotted against torque 
for a calibration curve. By this procedure, for increasing values, 
the motion of the transmission pulley or shaft is opposite to that 
for decreasing values. Hence both effects of friction, previously 
noted, are eliminated. 



K^i. 



9 DYNAMOMETERS 49 

For dynamometers with which the angle of torsion is read, 
the curve of torque vs. degrees may be used to get the spring 
constant. Then if S is this constant in pound-feet per degree 
of twist and A the torsion angle noted in usual operation, 

horse-power = .00019 XaSX A XR.p.m. 

which is the horse-power delivered by the dynamometer pulley. 

(b) Allowance for Friction, Windage, and Centrifugal Force. 
The readings of the dynamometer should be reduced by an amount 
corresponding to the torque necessary to overcome these forces. 
The values of the corrections may be determined as for weight- 
arm dynamometers. For recording instruments, a line should 
first be made on the chart with the dynamometer running free. 
The diagram under load should then be measured from this 
friction line as a datum. 

For dynamometers using a measurement of the torsion angle, 
the correction is made in degrees, being subtracted from the 
reading observed in operation. 

(c) Comparison with a Prony Brake may be made in exactly 
the same way as for weight-arm dynamometers. (Test 8 (d).) 

Problem 9i. The reading of a spring dynamometer running at 450 R.p,.m. 
is 26 degrees. If the spring constant is 3 lb. -ins. per degree, and if the cor- 
rection for windage, friction, etc., is 5 degrees, how many foot-pounds of 
work will be done in ninety seconds? What will be the horse-power trans- 
mitted? Ans. 22,200 ft.-lbs.; 0.45 H.P. 

Problem 82. Same data as Problem 9i, except that the friction of the 
transmission shaft is separately determined, the correction being 4 degrees, 
and the correction for friction of the indicating device is 1 degree. What 
is the transmitted horse-power when the torque is increasing? When it is 
decreasing? 

Problem 9.3. The axis of the piston p (Fig. 30) is 15 inches from the cen- 
ter of the driver shaft, and the diameter of the piston is 2 ins. Disregarding 
friction, what fluid pressure is produced when the horse-power is five, at 
150 R.p.m.? Ans. 44.0 lbs. per sq. in. 



50 



THE ENGINE INDICATOR 



10 



THE ENGINE INDICATOR- REDUCING MOTIONS 



The engine indicator is an instrument which makes a graphic 
diagram giving the relation between the pressure and volume 
of the fluid in an engine cylinder under working conditions. 
Since the area of such a diagram is proportional to work, the 

indicator is a dynamometer 
of a special type. It is 
shown in principle by Fig. 
31. C is a small cyUnder 
with a close fiUing piston 
P which is subject to the 
same fluid pressure as in 
the engine cylinder, being 
connected to it by a short 
pipe. This pressure compresses the spring S 
until the force of the spring balances the pressure. 
Thus the motion of the piston is proportional to 
the pressure. The piston motion is communicated 
and magnified by means of a linkage L bearing a 
pencil point at ^4. Z) is a metal drum free to 
oscillate on a spindle and carrying the paper on 
which the record is to be made. The drum is 
actuated by the engine cross-head through a cord K, a spring 
within the drum serving to bring it back upon the return stroke. 
Thus the motion of the drum is proportional to the engine pis- 
ton and therefore to the volume in the engine cyhnder behind dj 
the piston. The diagram made by the pencil point on the record 
paper is one of pressure shown vertically and volume (or piston 
stroke) horizontally. 

The principal use to which the indicator is put is the find- 
ing of the mean ejfedive pressure in an engine cylinder through- 
out its working stroke, from which quantity the cylinder or 




Fig. 31. — Engine 
Indicator. 



1 



10 



THE ENGINE INDICATOR 



51 



indicated horse-power may be calculated. (See Test 43.) Fig. 
32 is a typical indicator diagram from a steam engine. The 
average pressure on the forward stroke is the mean height, to 
scale, of the curve ahc. On the return stroke, the average pres- 
sure {hack pressure) is the mean height of cde. The effective 
pressure is the difference between these two, or the mean height 
of the indicator diagram. This may be found by dividing its 
area in square inches by its length in inches, and multiplying 
the quotient by the scale of pressure. The scale of pressure is 







Steam 


Line 






d 




Steam Valyei^ 
Closes-" \ 






^ 










.t 










•^ 














A^t 






1 








t 

<9 


1 




^^#^ 






e 


^rSham Vctlve 


"^"^"^"---^ 




I. 




Opens 






Q. 




Exhaust Yalve T 


X 




Opens ■-" 


\ 




Vv 






c 




'^ 


Exhaust Valve 








<^fe<--. 


y'" Closes ^ RETURN STROKE 


^ 










d Exhaust Line 










Atmospheric Pressure Line—^ 





Vo\ume 
Fig. 32. — Indicator Diagram from Steam Engine. 



the number of pounds per square inch on the indicator piston 
necessary to produce one inch of rise of the pencil, and is referred 
to as the spring scale. 

The indicator is equipped with a number of springs of different 
stiffnesses so that one appropriate to given conditions may be 
selected. 

The drum spring is adjustable so that a greater tension may 
be operative at higher rotative speeds to provide proper accelera- 
tion of the drum upon the return stroke. 



52 THE ENGINE INDICATOR 10 

The cord actuating the drum does not receive its motion 
directly from the engine cross-head, but from a reducing motion^ 
the function of which is to reproduce the engine stroke on a small, 
but always proportionate scale. A pantagraph is often used 
for this purpose. Under Tests 12 and 13 are described various 
types. 



10. Calibration of the Indicator Spring and Pencil 

Motion 

Principles. There are four causes of error in the ordinates 
of an indicator diagram. First, when applied to high speed 
engines, the inertia of the indicator piston and attached linkage 
causes a variation from correct positions. Second, at high speed, 
the pressure in the indicator cylinder lags behind that operating 
on the engine piston, because of the inability of the steam 
immediately to traverse the passages to the indicator. Third, 
the mechanism actuating the pencil may incorrectly magnify 
the motion of the indicator piston. Fourth, the spring scale 
may not be exactly known. Friction of the indicator piston and 
linkage causes a variation of the spring scale, since because of 
it the pencil is too low when rising and too high when falling. 
(See Test 2, principles.) 

The first of these errors may be avoided, or reduced, by the 
use of stiffer springs than are appropriate to low rotative speeds. 
With a stiffer spring, the total rise of the pencil is less, and there- 
fore the velocity and inertia of the pencil motion parts are 
decreased. 

The second cause of error, lag in the fluid pressure, may be 
reduced by the use of short and direct pipe connections between 
the indicator and engine cylinders. 

Errors due to the third and fourth causes may be corrected 
as will be described. 



10 THE ENGINE INDICATOR 53 

(a) The Pencil Motion may be Tested as Follows: With 

the indicator spring removed, a horizontal line is drawn on a 
piece of record paper placed on the drum, by revolving it by hand, 
the pencil bearing against the paper at a^low position of the 
linkage. Then, with the drum held stationary, a vertical line 
is made by moving the pencil and Hnkage up by hand. This 
is repeated with the drum in a second position. The two vertical 
lines should be parallel and straight, and perpendicular to the 
horizontal line, if the pencil motion is true. 

(b) Determination of Ascending, Descending, and Combined 
Spring Scales by Graphic Method. It is necessary to get a 
series of values of true pressures and corresponding heights of 
indicator pencil. The apparatus for varying and measuring the 
pressure should preferably be one using the same working fluid 
to which the indicator is subjected in practice, so as to duplicate 
the conditions of temperature and friction. Dead weights 
applied directly to the indicator piston are sometimes used, but 
these do not correctly reproduce the working conditions. Fig. 
33 represents a calibration apparatus using steam. The pres- 
sure is varied by manipulating valves A and B, an opening of 
A and closing of B having the effect of increasing the pressure 
in the large steam chamber, and vice versa. The measuring 
device is a set of known weights acting on a plunger of known 
area, from which the pressure balancing the weights may be 
figured. An accurate and precise Bourdon gage would serve 
the purpose as well. The gage shown in Fig. 33 is used to indicate 
the pressure in the chamber when the weights are not balanced, 
for convenience in manipulating the valves A and B, 

Using the caUbration apparatus, a diagram similar to Fig. 34 
is made on an indicator card. For the ascending pressures, the 
weight table must be balanced and rising very slowly when the 
line is drawn. Similarly, for descending pressures, the table 
should be gently falling. The table is revolved by hand to reduce 
friction at the plunger. 



54 



THE ENGINE INDICATOR 



10 



The heights of the Unes from the atmosphere Une are then 
measured to j^o in., and recorded on the diagram with corre- 
sponding pressures as in Fig. 34. These data are then plotted 
and results obtained as for Test 2 (a). 

(c) Spring Scales by Method of Least Squares. The same 
experimental data are used, but the results are calculated as for 
Test 2 (b), the value of F in the equations then being the observed 




frvfn Sfeam Line j 



Fig. 33.— Indicator Spring Testing 
Apparatus. 



,.68" -JJ0l-5d 



13J" 1:56 — 40 



,02. — !:°s:-3o 



0.^ ^i2Lja 



0.32 



0.34' 



Atmo sphere v 



10 



Fig. 34.— Calibration 
Records. 



pressure in pounds per square inch, and £, the height of the 
indicator pencil in inches. 

(d) Correction of Indicator Diagrams. Various methods, more 
or less accurate and laborious, have been proposed for applying 
calibration results to indicator diagrams. Generally, it is suf- 
ficient to use the combined spring scale with which to multiply 
the mean height to get the mean effective pressure, the error 
involved being within the limit of accuracy of power tests. But 
the combined spring scale represents the true scale of the spring 



10 



THE ENGINE INDICATOR 



55 



more nearly than it does actual conditions, since the method of 
figuring it eliminates friction. Strictly speaking, the ascending 
and descending scales should be used separately on the diagram, 
the former applied to the mean height of cde. Fig. 32, since the 
pencil is rising on that line; and the latter to the mean height of 
abc since there the pressure falls. But when the back pressure 
line is horizontal in large part, as it almost always is, the descend- 
ing scale applied to the whole diagram will yield a fair result. 
The indicator is sometimes applied to other than power 
measurements, for which a high degree of accuracy is desirable. 





Pressure 

Fig. 35. Fig 36. 

Correction of Indicator Diagrams. 

It is then necessary to reconstruct the diagram to get correct 
results. A method of doing this is as follows. Calibration 
data are obtained as previously described, and plotted as shown 
by Fig. 35. The range of pressure P for the calibration must 
be the same as that in the indicator diagrams to be corrected, 
and all operating conditions of the indicator during its test the 
same as when the diagrams are taken. It will be noticed that 
the descending curve of Fig. 35 is not straight, and is joined to 
the ascending curve. Careful experimentation will reveal these 
characteristics. Actually, there can be no unfilled gap between 



56 THE ENGINE INDICATOR 10 

the two curves, as there would be under the assumption that 
both are straight lines, an assumption, as was pointed out under 
Test 2, made only for convenience in approximately figuring 
the scales. 

Having plotted the curves according to Fig. 35, the ascending 
scale should then be obtained by either of the two methods 
(a) or (6) previously given. The caHbration curve is next laid 
alongside of the indicator diagram to be corrected as shown by 
Figs. 35 and 36. Now, the back pressure line is shown correctly 
to the ascending scale determined from the calibration. To 
represent a point a of the indicator diagram on this scale, the 
construction abbiai^ is used, the point ai, being the required 
corrected position of a. Enough points are corrected in this 
way to reconstruct the pressure line of the indicator diagram. 
The ascending scale will then apply correctly to the whole diagram. 

(e) Sampling. When there are a large number of diagrams 
for a single engine test, a few representative ones only are selected 
for reconstruction. Suppose, for instance, that there are 24 
diagrams and that the average of all their mean heights is H 
inches. Three of these should be selected as near as possible 
to this average mean height, and fairly representative in general 
proportions. These three diagrams are reconstructed and then 
the desired results obtained from them. 

To get the average of the mean effective pressure from all 
the diagrams without reconstructing all of them, the value H 
may be reduced in the proportion that the mean height of the 
three sample diagrams is reduced after reconstruction. The 
corrected value of H when multiplied by the ascending spring 
scale gives the corrected mean effective pressure. 

Problem lOi. The pencil of an indicator throws 2 ins. If the boiler 
pressure is 145 lbs., what should the spring scale be to give as high a diagram 
as possible? Ans.y 80. 

Problem 10:. The ratio of the pencil motion to the piston motion of an 
indicator is 6 : 1. The area of the piston is | sq. in. With a 30-lb. spring, 
the difference between ascending and descending positions of the pencil at 



11 THE ENGINE INDICATOR 57 

a given pressure is 0.04 in. If the friction is all at the piston, how much is 
it in pounds? Arts., 0.3 lb. 

Problem IO3. With the same indicator and spring at last problem, if 
the friction between the pencil point and the paper is 2 oz., how much differ- 
ence in the height of the pencil will this make? Ans. 0.042 inch. 

Problem IO4. With the apparatus of Fig. 33, what is the effect of friction 
at the plunger upon the apparent true pressure? What effect has this upon 
the calibration records? 



11. Testing the Motion of the Indicator Drum* 

Principles, When an indicator drum is driven by a cord 
attached to a reducing motion mechanically correct, the motion 
imparted to it is approximately simple harmonic. Upon the 
forward stroke of the engine, the cord is pulling the drum, and 
upon the return stroke, the drum spring is stressing the cord 
to keep it taut. Thus the cord is always under stress. If the 
stress varies, the cord will stretch according to such variation, 
and consequently the drum will not assume the correct positions 
it would have if driven by an inelastic connector. 

Stress in an indicator cord is the resultant of three distinct 
forces: namely, the drum spring tension, the force required to 
overcome the inertia of tlie drum, and the force to overcome 
friction at the drum spindle and at any guide pulleys used to 
guide the cord. The force of the spring increases with the for- 
ward stroke of the drum (the spring being wound up) and decreases 
upon the return. The variation is usually uniform with the 
motion. 

In general, at the beginning of the forward stroke, inertia 
increases the cord stress since, as the speed is increasing from 
zero to a maximum at mid-stroke, inertia effects a tendency of 
the drum to lag. Beyond mid-stroke, however, the speed is 
decreasing, and as the drum tends to exceed the velocity induced 

* For a more complete discussion of this subject see author's article in 
Power, Aug. 20, 1912. 



58 



THE ENGINE INDICATOR 



11 



by the cord, a slackening results. Upon the return stroke the 
force of acceleration varies in the same way as on the advance. 

The force of friction is always opposite to the drum motion 
and therefore changes its direction at each stroke. During the 
forward stroke it tends to increase the cord stress, and upon 
the return, to decrease it. 

These three forces are represented graphically by Fig. 37. 
The resultant stress in the cord equals their algebraic sum at 
any drum position. At low speeds, the force of acceleration 







Positions of Drum 
Crank End 








Resultant e 
oc=os*od-of. 



Head End 
■I 



— I _ J^^'^'^fS——~(£^'PJl. 



■^-U 



i2 



O^r 



Of: 



k - Forwanjl Stroke-- 




—Return Stroke ->H^g 



Fig. 37. — Variation of Forces on Indicator Card. 



is practically negligible; hence the resultant cord stress increases 
on the forward stroke, and decreases on the return with lowered 
values due to the reversal of friction. At high speeds, the force 
of acceleration reverses this variation as shown by Fig. 37. At 
some intermediate speed the force of acceleration and the spring 
tension nearly balance, so that the cord stress is approximately 
constant during each stroke, but a trifle less on the return because 
of friction. This is the speed at which the indicator drum is 
best adapted to work, since the more nearly constant the cord 
stress is, the less is its stretch and the consequent error. 



11 THE ENGINE INDICATOR 59 

Let us now compare the effects of a higher speed than this 
with the ideal condition of constant cord stress. The effect of 
speed is to increase the stress at the head end and decrease it 
at the crank end (see Fig. 37). At the head end, therefore, the 
cord is longer and the drum travels further in this direction. 
Similarly, at the crank end, the cord is shorter and the drum is 
pulled further toward that end. The net effect is to pull out 
the indicator diagram. Now, if the diagram were lengthened 
uniformly its proportions would remain correct, and there would 
be no error. Accordingly, if the cord were subjected to a uni- 
formly decreasing and increasing stress, and if its stretch varied 
directly with the stress, a correct diagram would result. It 
follows that, lacking such uniformity, the error of any point 
of the diagram should not be judged by the absolute stress or 
stretch at that point, but by the difference between this stress 
or stretch and that necessary to produce a uniform lengthening. 
It is seen from Fig. 37 that the resultant cord stress is greater 
than that necessary for uniformity on the forward stroke and 
less on the return. Hence, during the forward stroke, the cord 
is too long and a point on the indicator diagram is to the left 
and behind its correct position. During the return stroke 
the cord is too short; a point on the indicator diagram is to the 
right and again behind its correct position, since the motion is 
reversed. The net effect of the stretch of the cord, then, is to 
make the mean effective pressure appear smaller, and the cut- 
off, compression and release earlier than their true values. 

(a) Determination of Spring Tension. Since this varies 
through the drum stroke, its value at mid-stroke may be measured, 
or the average of the values at the ends of the stroke may be used. 
A spring balance of between 5 and 10 lbs. capacity should be 
fastened to the cord leading from the drum, and through it the 
drum pulled past the position at which it is desired to measure 
the spring tension. The reading of the balance is noted at the 
instant of passing this position. This equals the spring tension 



60 THE ENXtIXE INDICATOR 11 

plus friction. The spring is then allowed to reverse the motion, 
and another reading is taken, equal to the tension minus friction. 
The sum of these readings divided by two is the spring tension. 

(b) Determination of Dnmi Friction. The same method 
is used as for measuring the spring tension. The friction equals 
the difference of the readings divided by two. 

With an indicator properly lubricated and adjusted, and of 
good make, the friction should not exceed 5 or 10 per cent. When 
the cord rims over guide pulleys, however, the friction is greatly 
increased. When the friction is high, the cause should be looked 
for and remedied. 

(c) Testing Indicator Cord. Tie one end of about four feet 
of the cord to be tested to a fixed point on a bench or table, and 
the other end to a spring balance. Mark this end a few inches 
from the balance with a fine ink line, and under this line place 
a piece of paper or a foot-rule. Stretch the cord by pulling the 
balance horizontally until about 5 lbs. are indicated. Now 
reduce the force to about 1 lb. and repeat this procedure a few 
times. The elongation may then be noted for the applied range 
of stress. As the cord in the operation of the indicator is generally 
not stressed more than 5 lbs. or less than 1 lb., this range is 
appropriate. A good cord should not stretch more than 0.01 
in. per foot per pound, but grades will be found with four times 
this stretch and more. 

The elongation and contraction of the cord are very much 
greater at stresses less than 1 lb. On this account there may be 
marked^overtravel at the crank end of the drum motion ^sithout 
a visible slackening or vibrating of the cord when the indicator 
is in usual operation. 

(d) Adjustment of Drum Spring Tension. The indicator 
is put in working adjustment on the engine to be indicated, the 
piston spring omitted. Then b\' putting the engine on first 
one dead center and then the other, two vertical lines may be 
made on an indicator card to mark the extremes of travel of the 



11 THE ENGINE INDICATOR 61 

drum. When the engine is run, a horizontal Hne will overtravel 
the vertical ones, as was previously demonstrated, if the speed 
is enough to cause any inertia effect. The overtravel at the 
crank end should not be greater than 0.01 in. for each foot of 
cord, the cord being of good quahty. If the overtravel exceeds 
this, the spring should be tightened, until it is reduced to the 
named amount. 

The spring should not be any tighter than necessary, as this 
would increase the reaction on the drum spindle and therefore 
the friction. For different speeds, different spring tensions 
should be used. 

(e) Testing Drum Motion with the Drum Motion Tester. 
The apparatus shown by Fig. 38 was devised by the author for 




Tmrnnntmn mruimmm 
Fig. 38. — Smallwood's Drum Motion Tester. 

this purpose. A shaft S, the rotary speed of which may be con- 
trolled by a variable speed motor, actuates two similarly pro- 
portioned crank trains E and C, set exactly 90 degrees apart. 
The motions of the two cross-heads are thus exactly proportional 
at all parts of their strokes. The indicator drum D is oscillated 
by fastening its cord to a bracket B carried on an extension of 
the horizontally moving cross-head. The cross-head with vertical 
travel carries a pencil point P which traces a diagram on a card 
on the drum. A diagram thus obtained is one of cross-head 
motion shown vertically and drum motion horizontally. If 
a rigid connector between the drum and the bracket were used 
instead of the indicator cord, the motion of the drum would be 
exactly proportional to that of the pencil, and the diagram 



62 



THE ENGINE INDICATOR 



11 



would be an inclined straight line. The effect of an elastic 
connector, as cord, variously stressed, is to give a curved Une. 
If a straight line is drawn between the highest and lowest points 
of this curve, then the horizontal departure of any point on the 
curve from the straight line shows the error in the drum motion 
at that point. 

When testing a drum motion for errors in an indicator diagram 
previously obtained, great care should be taken to reproduce 
all the operating conditions, relative to speed, spring tension, 
length of diagram, length of cord, general adjustment, and 



^^"^v^^.-.-Lenafh o-fDrum Motion, tio Speed— ->\ , 

W-^ Oyer-trdvel>\ K- 

Fu]l'6ffvk€~oTCro66l^e7oi 






Error on Return 6iroke'y\ K 
•• ** Forward " ->|l<| 



Head End 




Drum Mo+i 



/Forward 
'0" I Return 



Crank End 



Fig. 39. — Error Diagram from Drum Motion Tester. 



friction. Special care should be taken to reproduce the arrange- 
ment of guide pulleys. The effect of guide pulleys, especially 
if near the indicator, is similar to that of drum spindle friction 
and imposes an additional tightening force on the forward stroke 
and slackening one on the return. Fig. 39 shows a typical error 
diagram taken with the drum motion tester and is self explanatory. 
In some cases the drum advances its correct position instead 
of lagging behind it on the return stroke. This is caused by the 
departure of the acceleration force from the variation assumed 
in Fig. 37, because of abnormal stretch of the cord and the con- 
sequent change in the drum velocities. 



11 



THE ENGINE INDICATOR 



63 



(f) The Correction of Indicator Diagrams from Drum Motion 
Tester Records may be accomplished as shown by Fig. 40, which 
needs no comment. Samphng of the diagrams may be done as 
indicated under Test 10 (e). 



ERROR DIAGRAM 




Full lines ^How di a of rams 
as fdkcn. 
Doffeof lines sS ho yv 
corrected oliaofrdms. 




Fig. 40. — Correction of Indicator Diagrams. 



Problem lli. The force of acceleration of the indicator drum varies 
directly with its stroke and the square of the engine R.p.m. If a drum 
motion with a 4-in. stroke is designed correctly to operate at 200 R.p.m., 
how long should the stroke be to operate correctly at 250 R.p.m.? At 300 
R.p.m.? Ans., 2.56 in.; 1.78 in. 

Problem II2. What should be the constant of a drum spring (pounds 
per inch of extension measured on the card) to balance throughout a 4-in. 
stroke a force of acceleration which has a maximum value of -fl lb. at the 



64 



THE ENGINE INDICATOR 



12 



head end, and —1 lb. at the crank end? If the engine R.p.m. is doubled, 
what should be the constant of the spring? Arts., 0.5 and 2.0 lbs. per in. 



12. The Testing of Link Type Reducing Motions 



Principles. The pantagraph in various forms has been much 
used to reduce engine cross-head motion for the purpose of driving 
indicators. Fig. 41 shows a number of them, diagrammatically. 
In these and in the following two figures, the letter F denotes 
the fixed center of the linkage; R, the point at which the indicator 
cord is attached; and C, the point of attachment of the hnkage 
to the engine cross-head. 

R 




Fig. 41. — Pantagraph Reducing Motions. 

There are two conditions necessary to the proportionaUty of 
motion of the points R and C. First, they must lie on a straight 
line passing through F, and second, the links that are parallel 
in one position must remain so in all positions. 

Fig. 41 A and B are familiar forms, the reduction of motion 
being in the proportion of FR to FC. The identity of Fig. 41 C 
may be established by the dotted lines, the linkage thereby repre- 
sented being replaced by the sliding bar on which the point R 
is centered. With this arrangement, the ratio of the long to 
the short link below F must be equal to the corresponding ratio 
above, in order to fulfill the condition of parallelism. This reduc- 
ing motion is appropriate to high speed engines since by it only 



12 



THE ENGINE INDICATOR 



65 



a short length of cord need be used. Fig. 41 D is a convenient 
form of pantagraph made by attaching to the engine crank shaft 
a small eccentric and rod, or crank and rod, the throw of which 
is equal to the desired drum stroke. It will be seen that for a 
correct reduction, the eccentricity must be in line with the engine 
crank; and the ratio of the lengths of eccentric rod to eccentricity 
must equal the ratio of the engine connecting rod to crank length. 
Fig. 41 £' is a modification of this, the motion being the same as 
that of a Scottish yoke, that is, a crank train with infinitely 
long connecting rod. The motion is therefore inaccurate. 

In each case, the proportional motion of R is parallel to 
that of C. Therefore, the indicator cord should be led from the 
reducing motion parallel to the cross-head guides; if on a slant, 
the drum motion will not be proportional to the cross-head 
motion. 

Reducing motions of the pendulum type are represented by 
Fig. 42. By A is shown the slotted pendulum. The shorter 



— R ^-« — 







Fig. 42.— Pendulum Reducing Motions. 



is the indicator cord, the greater will be its angularity due to the 
circular motion of R, The motion of R is not truly proportional 
to C since the ratio of FR to FC varies. Fig. 42 B shows the 
slotted cross-head, a correct motion except for the angularity 
of the cord. Fig. 42 D is the same as C except that a ^' brumbo '' 
pulley is attached, by which the cord may be led off at an angle 
with less error than if the pulley were not used. With a horizontal 



66 THE ENGINE INDICATOR 12 

cord, the pulley causes more error than would be obtained with- 
out its use. 

The errors of these reducing motions are kinematic and 
mechanical. Mechanical errors are due to lost motion in the 
joints, or flexing of the links. Kinematical truth or errors 
depend on the design. 

(a) Calibration by Line Diagram. The crosshead motion 
is laid out to scale as shown by XY, Fig. 43, and divided into a 

number of equal parts. The centers of 
\^ the reducing motion are then located to 

l\ represent it in an extreme position, and 

\\ "^"^ ^ point D to show the corresponding 

I \ position of the indicator drum. A second 

\ \ position of the reducing motion is tlien 

l \ drawn and a second drum position marked, 

\ \ and so on. It is then an easy matter 

— -'^-t^tt: ^^-^^-^^^^ c ^o measure the error of any of the drum 

positions since the distances between them 

Fig. 43. should be equal for exact proportionality 

of motion. If desired, the data may be 

plotted the same as Fig. 39, from which indicator diagrams may 

be corrected according to Test 11 (/). 

(b) Calibration by Direct Measurement. The indicator and 
reducing motion are set up as in actual use. The dead center 
positions of the engine cross-head are marked on the cross-head 
guides against a datum line on the cross-head. With the cross- 
bead placed at any part of its stroke, its position may then be 
readily measured from either dead center and expressed in per 
cent of the stroke. For a proportional motion, the indicator 
drum should have moved from its corresponding dead center 
position (located by marking with the indicator pencil a vertical 
line on a card on the drum) the same percentage of its stroke. 
A number of such measurements at different parts of the strokes 
furnish data which may be applied the same as under (a). 



L 



13 THE ENGINE INDICATOR 67 

Care should be taken that motion is not lost through stretch 
of the indicator cord. For rehable results, wire should be used 
between the reducing motion and the indicator drum. If the 
wire is not sufficiently flexible to pass around the drun, a few 
inches of cord tied to the wire may be used for this purpose. 

Problem 12i. The stroke of the drum given by the reducing motion of 
Fig. 41 £' is 4 ins. The ratio of the engine connecting rod to crank length is 
5:1. Figure from the kinematic formulas the maximum error in the drum 
motion. 

Problem 122. Is the best arrangement of Fig. 42 C with the lower link 
always above the horizontal, always below it, or partly above and partly 
below? Why? What effect has the length of this link upon the accuracy 
of the motion? 

Problem I23. Draw two indicator diagrams, superimposed, to show 
the effect of twisting the eccentric of Fig. 42 D ahead of the crank by 10 
degrees. 



13. The Testing of Reducing Wheels* 

Principles. Link reducing motions have been largely sup- 
planted by reducing wheels on account of the latter's ready 
adaptability. This type of motion consists, in general, of two 
drums of different diameters mounted on separate shafts that are 
connected together with gears. Fig. 44 shows them on the same 
shaft for simplicity. The indicator cord is led from the engine 
cross-head to the larger drum to which it is fastened. Another 
cord connects the smaller drum to the indicator drum. It will 
be seen that the velocity of the one cord is to the other as the 
ratio of the drum diameters of the reducing motion. The reduc- 
ing wheel is supplied with a spring which acts the same as the 
indicator drum spring. One of the reducing motion drums 
is made interchangeable with others of various diameters so 
that different reductions may be made. 

* For a more complete discussion of this subject, and experimental results, 
see author's article in Power, Sept. 24, 1912. 



68 



THE ENGINE INDICATOR 



13 



In the operation of a reducing wheel the same forces are at 
work as in the case of the indicator drum (Test 10, principles), 
namely, spring tension, friction, and the force due to inertia. 
Since the indicator drum and wheel masses are connected by a 
short cord having inconsiderable stretch, they may be regarded 
as one mass producing a single inertia effect. Likewise, the 



Fbrward stroke ' 




-Indicaivr 
Drum 



Head End Midsfrt>ke Crank End 

V- -Yelociiy Increa^irfG^ - ->j— -Vdocify Decreaiincf- - ->j 

CD 



Enofine 
Cro6shead 



Inerfia • 
Sprinof Tension 
Friction ■ 



Resultant on Cord <- 



Forces a+ Wheel 



'Return Stroke 



k - Velocity Decreasing ^ - Vehciiy Increasing -iA 




Inertia 

Sprincf Tension 

Friction 



^0 



Resultant on Cord ^-^ 
Fig. 44. — Forces on Cord Driving Reducing Wheel. 



two springs may be considered as exerting a single force. In 
Fig. 44, the component forces are shown as they are felt at the 
cord at three parts of each forward and return stroke. The 
arrows represent roughly by their length the comparative 
magnitude of the forces. 

At the beginning of the forward stroke, the cord exerts a 
maximum force in overcoming friction, inertia and spring ten- 



L 



13 THE ENGINE INDICATOR 69 

sion, but as most of the cord is wound on the wheel, its stretch 
and the consequent lag of the drum are inappreciable. 

As the cross-head advances, the length of cord free to stretch 
becomes greater, but, as the velocity of the moving parts 
approaches its maximum in the neighborhood of mid-stroke, 
the effect of inertia is to lessen the force exerted by the cord 
and therefore its stretch. This continues throughout the for- 
ward stroke; as the length of the cord increases its stress decreases, 
and the net effect is to maintain a reasonably uniform total 
stretch and consequently to give a correct drum motion. On 
the return stroke, however, the spring tension is required to 
accelerate the wheel sufficiently so that the cord does not slacken, 
and it must do this not only against inertia, but against the 
frictional resistance. 

As the friction is large, the spring may not be able to do 
this at a rate equal to that at which the cross-head is being 
accelerated, particularly at the beginning of the stroke, as here 
the acceleration is greatest. The stretch of the cord is therefore 
released at the beginning of the return stroke, if not entirely 
slackened, as evidenced by whipping. Beyond mid-stroke, 
the moving parts of the wheel have gained sufficient momentum 
to draw up the cord again, and this momentum keeps it taut 
to the end of the return stroke. Under ordinary circumstances, 
then, a marked distortion of the drum motion may be expected 
only through the return stroke and greatest at its beginning. 

Obviously the length of the cord free to stretch, i.e., that 
part of it not wrapped around the wheel, has a decided influence 
upon the correctness of the motion. In practice this length 
at its minimum and maximum is determined by the engine stroke. 
Ordinarily, at the head end, the length of cord free to stretch 
is about equal to the stroke, and at the crank end twice 
as long. 

Experiments upon reducing wheels will disclose the following 
characteristics. 



70 THE ENGINE INDICATOR 13 

First. The overtravel of the indicator drum is small at both 
ends of the stroke. 

Second, The distortion of the return-stroke motion is very 
marked and follows a characteristic wave. The forward motion 
is in all cases very closely true. 

Third, The piston speeds producing whipping and therefore 
limiting the operation of the wheel, are much greater at the longer 
strokes. 

The first effect is largely due to friction which helps the 
springs to check the velocity of the wheel at the end of the for- 
ward stroke. Much overtravel at the crank end would be 
evidenced by whipping of the cord. For instance, if the drum 
motion were 4 ins. and the engine stroke 24 ins., an overtravel 
of the drum of J in. would mean a slackening of the cord six times 
that amount, or f in., since any distortion of the drum motion 
is multiplied at the wheel by the ratio of the motions. This is 
enough to cause whipping unless the cord is very stretchable. 
At the head end the overtravel is subdued not only by friction 
but l3y the positive resistance of the cord, the stretch of which 
is a minimum at this end because of its reduced length. 

Overtravel of the drum motion does not indicate error with 
reducing wheels, as it is always small, exists for even low speeds 
when the motion is actually accurate, and may not exist at 
all when the friction is such as to cause large error. 

The second effect is due not only to friction, but is increased 
because an indicator cord varies very considerably in length 
for changes of stress below 1 lb., although above that amount 
the stretch is comparatively small and uniform with increasing 
stress. Also the cord will contract markedly when the stress 
reduces to zero, and sometimes has been observed to continue 
contracting after the stress was entirely removed. If the fric- 
tional resistance to motion of the reducing wheel prevents the 
spring from properl> accelerating it upon the return stroke, 
the cross-head motion gains upon the wheel motion, thus reduc- 



13 THE ENGINE INDICATOR 71 

ing the stress in the cord, perhaps to only a few ounces. The 
cord accommodates itself to this change in length because it con- 
tracts markedly at low stresses, and not until the distortion of, 
the drum motion is quite pronounced is the speed of contraction 
exceeded by the cross-head speed, as evidenced by whipping. 

The lag of the drum motion just after passing the crank- 
end dead center is only momentary at moderate speeds because 
the force required to accelerate the wheel is a maximum at dead 
center; when it has once started upon the return stroke less 
force is needed to continue the motion and this the spring is able 
to deliver. At higher speeds the action of the spring is further 
delayed, so that the late acquired momentum of the parts causes 
them to overshoot the mark and fetch up against the positive 
resistance of the cord, resulting in the wave effect. 

The third effect follows from the limitations caused by inertia. 
It may be explained by the fact that at a given piston speed the 
oscillations per minute of the wheel are greater the smaller the 
engine stroke, and therefore the effect of inertia is greater Avith 
the small strokes. Obviously, it is more difficult to oscillate 
a mass moving at a fixed average speed, the more frequent are 
the oscillations. This also follows from the mathematical value 
for the force required to accelerate a reducing wheel at the ends 
of the stroke (assuming harmonic motion) v/hich may be expressed 
as follows: 

A = WXLX N^ X a constant 

in which 

A = Force of acceleration referred to the cord; 
W^ = Weight of moving parts referred to the cord; 
L = Length of engine stroke; 
A/' = Revolutions per minute. 

In this expression LN is proportional to the piston speed. The 
force A cannot be greater than a certain value which Umits the 



72 THE ENGINE INDICATOR 13 

operation of the wheel. The product LN will have a maximum 
value, corresponding to the limiting value of ^, by increasing^L 
rather than A^, since A varies as the first power of L, and as the 
square of N, 

This analysis does not consider the inertia of the indicator 
drum. The throw of the drum is practically constant at all 
strokes, so the force required to accelerate it at the ends of the 
stroke is 

a = u; X Z X A^^ X a constant 
or 

a = ir X y^ X a constant 

in which w is the weight of the drum and I its stroke. Thus, a 
varies with the square of the R.p.m. onl3\ 

The total force of acceleration of drum and wheel is the sum 
of these forces a and A, but as the drum spring is strong enough 
to meet the drum inertia at the highest speed of oscillation possible 
with the usual reducing wheel, the force a generally need not be 
considered. 

If the wheel velocities are low so that inertia is not material, 
the frictional resistance to motion, if excessive, may cause a mate- 
rial lag of the drum behind its correct position throughout both 
strokes, since it effects a stretch of the cord upon the forward 
and a slackening upon the return stroke. 

If the variation of stress in the cord is the same for different 
engine strokes, the distortion of the drum motion is the same. 
This is because any error in the motion of the wheel is reduced 
at the drum in the ratio of the drum travel to the wheel travel. 
For example, if the stresses are the same, the stretch of the 
cord on a 4-ft. engine stroke is doul)le that of a 2-ft. stroke, since 
the cord is twice as long, but as the resulting drum distortion 
is Vu of the stretch in the one case (drum stroke being equal to 
4 ins.) and \ in the other, the effect is the same. 



13 THE ENGINE INDICATOR 73 

(a) Determination of Spring Tension and Friction. The 

method is the same as described under Test 10 (a) and (6). The 
friction in a well designed wheel is not likely to be less than 20 
per cent of the spring tension, and may be as much as 50 per cent 
in poor designs or when the reducing wheel is badly assembled. 
As the greatest source of error is in friction, this test is an important 
one and furnishes a good indication of the merit of a reducing 
wheel. 

When the wheel spring tension cannot be made great enough 
to accelerate the parts correctly, the deficiency may be made 
good by tightening the indicator drum spring, to a limited extent 
only. The drum spring acts upon the wheel at a mechanical 
disadvantage on account of the reduction of motion, and therefore 
has only a small effect to accelerate it. On the other hand, 
tightening the drum spring increases the reaction on the drum 
spindle, and therefore the friction to be overcome throughout 
the stroke, and this may cause even more distortion. As a gen- 
eral rule, it is best that the indicator drum spring have only just 
sufficient tension to overcome its own inertia. The wheel spring 
tension should be as high as possible if its ability to accelerate 
the wheel parts is doubted. 

(b) Testing Reducing Wheels with the Drum Motion Tester. 
To adapt this device. Fig. 38, to reducing wheels, a bracket, or 
some equivalent attachment is necessary with a long stroke 
to duplicate an engine cross-head motion; and, to make the 
apparatus cover all operating conditions, the stroke should admit 
variation. This is conveniently accomplished by coupling an 
extension rod to the motion tester, carrying at its outer end a 
rack meshing with a pinion on a vertical shaft. This shaft 
Sj Fig. 45; carries a wooden disc replaceable by others of different 
diameters. When the rack is reciprocated, the disc is given 
an oscillating motion. An extension of the indicator cord from 
the reducing wheel being fastened to a point on the circum- 
ference of the disc, the cord will be reciprocated through a stroke 



^ 



74 



THE ENGINE INDICATOR 



13 



the length of which depends upon the diameter of the disc. 
By using different discs, a reducing wheel may thus be operated 
through any desired stroke. 

The reducing wheel to be tested is connected to an indicator 
and the whole set in place on the tester. The wheel may then 
be operated at any required conditions of stroke, speed, and cord 
length; and error diagrams similar to Fig. 39 taken. The cord 
length may be fixed by tying the desired length to a piece of 
stranded wire the other end of which is attached to the disc 



PLAN 
-Wire fasfemed here 




Dnvincf Shaif -W^ 

Variable Speed [-'-^ 




a=^ 



ELEVATION 



(Pencil ortE 
Indicator rt-y^A K; 




Wf^'-Rack 

TTTTTmmTTTTTTTTTTm 



TmrrTTTTTTumnTmrn jujurn ;/;/n/i/;//i///////;/// 



Fig. 45. — Smallwood's Drum Motion Tester Applied to Reducing Wheels. 



of the tester. The wire being practically inextensible, the effect 
is to reciprocate the cord through the desired lengths as by an 
engine cross-head at A', Fig. 45. 

Fig. 46 shows a number of error diagrams taken in this way. 

(c) Correction of Indicator Diagrams. This may be done as 
described under Test 11 (/j. The reducing wheel is reasonably 
accurate on short engine strokes and moderate piston speeds, 
and on long engine strokes at all usual piston speeds if properly 
designed to avoid friction. The drum motion resulting from its 



13 



THE ENGINE INDICATOR 



75 



use has its maximum error, when the friction is small, at a part 
of the stroke where usually it would affect the indicator dia- 
gram little if any, namely, at the beginning of the return stroke 
where either the steam line on the crank end or the exhaust line 



Overfrcxvef mecxsured 
from this line 




Fig. 46. — Error Diagrams from Reducing Wheels. 



on the head end diagram is described. As these lines are generally 
horizontal, or nearly so, errors upon them would not appear, 
except at their ends. 



76 PLANIMETERS 14 



IRREGULAR AREAS AND MEAN HEIGHTS 

Numerous engineering instruments, of which the engine 
indicator is one, have been devised to give an autographic diagram 
of the measured quantity expressed as an ordinate, the abscissae 
being generally time or in linear units simply. From such a 
diagram it is often desired to get the mean value of the measured 
quantity, that is, the mean ordinate of the diagram to scale. 
For this purpose, planimeters are used. Some planimeters 
measure the mean ordinate directly; others measure the area 
of the diagram, from which the mean ordinate may be found 
by dividing by the length. The best known of these two types 
are the Amsler Polar planimeter and the Coffin averaging instru- 
ment. The former is used to measure any irregular area; the 
latter is applied chiefly to the determination of the mean height 
of indicator diagrams. 

14. The Polar Planimeter 

Principles. Fig. 47 shows in diagram the Amsler planimeter. 
When the tracing point traverses any closed curve, 1-2-1 the 

record wheel follows in a certain 
-n^^ en er i^2ii\\ and, through contact with the 

surface upon which it bears, is given 
a motion partly rolling and partly 
sliding. The principle upon which 
the instrument depends is that the 
^'hed- \ J^^^^ rolling motion of the wheel is directly 

proportional to the area circum- 

jracin^^Point-' scribcd by the traciug poiut. If, then, 

Fig. 47.-Polar Planimeter. ^lie wheel is properly graduated, the 

area may be read directly. 
When the area to be measured is comparatively large, the 




14 PLANIMETERS 77 

fixed center of the instrument is placed within the area, thus 
securing a greater reach of the tracing point. (See Fig. 51.) 
In this case, the readings of the wheel must be interpreted dif- 
ferently and the constant known as the 
zero circle must be known. The zero 
circle maybe defined as one of such size i j\\^n;^ zero 
that if the fixed center of the planimeter ■ ^ ^ ^^■ 




is placed at its center, and if the tracing 

point then traverses its circumference, 

there will be no. motion of the record 

wheel. It may be seen from Fig. 48 

that this condition requires that the plane of the record wheel 

shall pass through the fixed center, for in this position the wheel 

will travel in the direction of its own axis and there can therefore 

be no rolling. 

The algebraic expression for the radius of the zero circle 
may be deduced as follows. (See Fig. 48.) 

ro^=x^ +(6+c)2 

-(a2~62) + (52+2&c+c2) 

= a^+(P+2bc (1) 

To deduce the mathematical relation between the area cir- 
cumscribed by the tracing point and the circtunferential motion 
of the record wheel. There are two cases, namely, the fixed 
center within and the fixed center without the area circum- 
scribed. The following paragraph gives an outline of the deduc- 
tion for the first case. 

1. The motion of the tracing point is referred to polar coordi- 
nates whose pole is at the fixed center of the instrument. A polar 
differential of area is considered as the one circumscribed by the 
tracing point. An algebraic expression for this area is obtained 
in terms of the polar coordinates. 2. An expression is deduced 
for the motion of a point on the record wheel circumference in 



78 PLANIMETERS 14 

terms of the constants of the instrument. The motion is that 
which takes place when the tracing point has outhned the differ- 
ential of area. 3. By comparing the two expressions (for the area 
and for the motion of the wheel) the desired relationis obtained. 
Fig. 49 shows the differential of area, marked 4-5-6-7. Using 
the notation of the figure, 

Area 1-4-5 = ^r • rdK = \rHK 
Areal-7-G = ^n^K 

Subtracting, Area 4-5-6-7= \dK{r'^-ri^), ... (2) 

This is the expression for the differential of area. 

Consider now the corresponding motion of the record wheel. 
It is to be observed first that this is not affected by the radial 

motion of the tracing point. The angle 
between the arms when the point is at 4 
(Fig. 49) is the same as that at 5. The same 
applies to points 6 and 7. Hence, the motion 
of the wheel when the tracing point passes 
on the radial from 5 to 6 is the same as that 
when it passes from 7 to 4. But as these two 
motions are opposite, they neutralize each 
other. The same reasoning applies to any 
irregular area as in Fig. 47. The radial 
component of the motion from 1 to 2 is the same in amount as 
that caused in passing from 2 to 1, but opposite in direction. 
So we may altogether disregard the motion of the wheel produced 
by the radial motion of the point. 

Considering again the differential of area of Fig. 49, it is 
seen that the motion of the tracing point from 4 to 5 is greater 
than that from 6 to 7, and that the angle made by the arms is 
different when the point traverses the two arcs. Hence the 
circular component of the motion of the tracing point when traver- 
sing a closed curve produces a record on the wheel. We have, 
then, to consider the effect of this component. 




14 



PLANIMETERS 



79 



See Fig. 50. The record wheel moves from 2 to 2' when the 
tracing point passes from 4 to 5. The rectangular component 
of the motion, 2-2', causing rotation of the wheel, is represented 
by the line m, perpendicular to the wheel axis, m is therefore 




Fig. 50. 



the distance moved through by any point on the record wheel 
circumference relative to its axis. 



From 1-2-3, 
From 1-2-4, 

Subtracting, 
From which. 

From (1), 



m = XdK sin (A -90°) 
= —X cos AdK 

a2 = 62 +X^-2bXcosA. 
r2 = (6+c)2+Z2-2(6+c)XcosA. 
q2_j,2 =,_25c — c^ +2cXcosA. 

XcosA= y(a2+c2+26c-r2). 

1 



= 2c^ro^-r^) 



(3) 



(4) 



80 



PLANIMETERS 



14 



Combining (3) and (4) 



m = ^(r^-ro^), 



(5) 



which is the value for the rotation of a point on the circumference 
of the record wheel when the tracing point moves from 4 to 5. 
Similarly, when it moves from 6 to 7, the motion is 

The difference between these two motions, m and mi, is the 
resultant motion M of a point on the circumference of the record 
wheel when the whole area has been circumscribed, or 



M=m—mi = 
Comparing (2) and (6) 



2c 



(6) 



Area 4-5-6-7 =^{r^- n^) • - 
2 c 



= Mc, 



(7> 




Fig. 51. 



which is the required relation. 

The deduction of the relation for 
the second case, namely, when the 
fixed center is within the area to be 
evaluated, is similar. Under this con- 
dition, however, the circular component 
of the tracing point is always in one 
direction. Hence there is no subtrac- 
tion as indicated by equation (6) and 
the differential expression is 

M = — (r2 — ro^). 



14 PLANIMETERS 81 

Integrating this for the entire circumferential motion of a point 
on the circumference of the record wheel, 



^=r' 


dK r2 n 
2c Jo 


2c 


-f: 


'rf(area) 
c 


T 


2c 


area 
c 


2W. 
2c 












From which, 


Area = 


--Mc-\-irr(?, 


• • 


• • 


• • • 



(8) 

which is the required relation. 

From these two deductions it is seen that, 

First. When the fixed center of the planimeter is without 
the area to be integrated the motion of a point on the circum- 
ference of the record wheel, relative to its axis, multiplied by the 
length of the arm c, equals the desired area. 

Second. When the fixed center of the planimeter is within 
the area to be integrated, this product added to the area of the 
zero circle equals the desired area. With the working form of 
the instrument, the multiplication Mc is not necessary, the wheel 
being graduated in terms of square inches, or other units of 
area. 

In some types of polar planimeter, the arm c is made adjust- 
able in length, so that areas drawn to various scales may be read 
directly. 

(a) Determination of the Zero Circle. If the lengths of 
the arms, a, 6, and c, are carefully measured, the radius of the 
zero circle may be computed by means of the relation given by 
equation (1), and from this the area. 

If the axis of the wheel is in a perpendicular plane through 
the arm c, the graphic method suggested by Fig. 48 may be 
used. Two lines are drawn at right angles to each other, the 
fixed center placed on one, the tracing point on the other, and 
the point of contact of the wheel and the paper at the intersec- 



M^ 



82 PLANIMETERS 14 

tion of the lines. The radius of the zero circle is then the dis- 
tance between the fixed center and the tracing point. If the 
axis of the wheel does not lie in a vertical plane through the arm 
c (as is sometimes the case) the construction must be altered to 
allow for this difference. 

Another method consists in comparing the indications of the 
planimeter with the calculated area of a circle larger than the 
zero circle, the arms of the instrument being clamped for con- 
venience when describing the circle with the tracing point. If 
the indication of the planimeter be subtracted from the cal- 
culated area, the result will be the area of the zero circle. This 
follows from equation (8). 

When traversing a large circle, the fixed point being at the 
center, the clamping of the arms may be accomphshed by placing 
the fixed and tracing points in two holes pierced in a strip of 
manilla paper; these holes being distant from each other an 
amount equal to the radius of the traversed circle. 

(b) Comparison of Instrument Indications with Known 
Areas. For this purpose may be used a check rule, an in- 
strument by which the tracing point of the planimeter may be 
swung through a circle of known radius. Initial and final 
readings of the record wheel are taken; the difference between 
these readings should equal the area traversed. When the 
fixed center of the planimeter is inside the area, the difference 
between the readings should be added to the area of the zero 
circle. 

If the instrument indications do not correspond to the actual 
areas, the length of the arm, c, should be adjusted. 

Notice that the wheel reads positively if the direction of the 
tracing point is clockwise, with the single exception of the case 
when the area to be integrated is less than the zero circle and 
the fixed center is inside the area. 

It is well always to traverse the area in a clockwise direction 
and to use the following forms : 



14 PLANIMETERS 83 

Area = second reading — first reading, 
or 

Area = second reading — first reading+xro^. 

As an exercise record the results of two or three area readings 
of the following and compare with their calculated values. 
Small circle, fixed center outside. 
Circle > zero circle, fixed center inside. 
Circle < zero circle, fixed center inside. 

Note Carefully. Do not put down the result of an area only, 
but record in tabular form, as follows: 

1st Reading. 2d Reading. Result. 

(c) Comparison of Instrument Indications with Areas to 
Scale. Planimeters with adjustable arms generally are arranged 
to be applicable to various scales. For instance, for a certain 
adjustment, each graduation of the wheel may indicate one 
square foot on an area drawn to a linear scale of | in. equals 
1 ft. For comparison the check rule may be used, its area 
in square feet on a f-in. scale being figured by multiplying 
its area in square inches by the square of the linear scale, that 
is, 16. 

As an exercise, compare the planimeter and calculated 
results of a circle larger than the zero circle, using the scale 
setting. 

(d) Arm Adjustment to a Required Scale. Suppose it is 
required to read areas to a scale not provided for by the markings 
of the adjustable arm. The necessary length of the arm c 
may be calculated from equation (7). In this equation, we may 
assume the area to be one square inch. Then the motion M equals 
the length of one graduation on the wheel multiplied by the 
number of graduations previously selected to represent the scale 
units in one square inch. 



84 PLANIMETERS U 

Let w = diameter of record wheel, inches. 

G = number of graduations on the record wheel. 

X = number of graduations representing one scale unit of 

area. 
Y = number of scale units of area in one square inch. 

Then, length of one graduation = -^ in inches. 

When the tracing point traverses one square inch of area, the 
number of graduations corresponding to the motion, ilf , will be 
XY; and 

M='^XY. 

(jT 

From (7) ^XYc = 1 sq. in., 

and c = 



TTWXY' 



in which everything is known except c, which may be found. 
A convenient application of this principle is in the direct 
determination of horse-power from indicator diagrams, for 
which purpose the arm c should be adjusted to the length given 
by the following formula. 

10500Z^ 
^" SKwX' ^^^ 

in which G, Wj and X are as previously defined, and 

Z= length of the indicator diagram, inches, 
*S = scale of the indicator spring, 
K = product of LAN in the PLAN formula (see 
Test 43). 



14 PLANIMETERS 85 

Problem 14i. Deduce the equation for the zero circle of a planimeter 
having the record wheel between the pivot and the tracing point instead of 
as shown by Fig. 48. 

Problem 142. If a is 5 ins.; 6, 2 ins.; and c, 3 ins., what is the area of the 
zero circle applicable to an arm adjustment for a J in. = 1 ft. scale? 

Arts., 2310 sq. ft. 

Problem 143. The fixed center of a planimeter is inside an area to be 
integrated which is smaller than the zero circle; consequently the wheel 
rotates backward. The first reading is 29.23 sq. ins.; the second, 48.73 
sq. ins. What is the area if the zero circle area is 212 sq. ins.? 

Ans. 132.5 sq. ins. 

Problem 144. Integrate the area enclosed by a loop like a figure 8, first 
by finding separately the areas of the loop, and second by tracing the loop in 
the direction of its curve. Account for differences. 

Problem 145. The arm c of a planimeter is 2.0 ins. long and the diameter 
of its record wheel is 0.79 in. How many turns will the wheel make when 
the tracing point circumscribes 117 sq. ft. to a |-in. = 1 ft. scale? 

Ans. 13.1. 

Problem 146. If the wheel diameter is 0.79 in., what should be the length 
of the arm c so that one revolution corresponds to 1000 square miles on a 
hnear scale of i in. = 1 ft., there being 100 graduations? Ans.j 6.25 ins. 

Problem I47. Deduce equation (9). 

Problem 148. Find the mean height of a given indicator diagram with 
a planimeter. Calculate the horse-power. Find the horse-power by adjust- 
ing the arm as described under (d). Compare results. 



15. The Coffin Planimeter 

Principles. Fig. 52 represents this planimeter. It consists 
of a single arm one end of which carries the tracing point, the 
other end bearing on a pin which sUdes in a guide represented 
by the line gg. The record wheel is mounted on the arm as 
shown. An examination of Figs. 52 and 47 will show that the 
Coffin planimeter is the same in principle as the polar; the 
mechanical difference being that the arm a of the former is infinitely 
long, so that the pivot swings in a right line instead of the arc 
of a circle. The relation Mc = area therefore applies (see Test 
14, principles). 

The instrument may be used for finding areas, but its chief 
use is in determining the mean heights of indicator diagrams. 



86 



PLANIMETERS 



15 




--Record Wheel 



^■■^Udincj Pin 



Fig. 52. 
Coffin Planimeter. 



For this purpose the indicator diagram is arranged as shown 

by Fig. 53, with its left-hand extremity in the line of the guide, 

and its base perpendicular to the line 

of the guide. The tracing point of the 

planimeter is then placed at the extreme 

right-hand point of the diagram, 1, 

and an initial reading taken. Next, 

the figure is traced in a clockwise 

direction, until the tracing point comes 

back to the point, 1. If now the 

tracing point is moved on a line parallel 

to the guide line until the wheel indi- 
cates again its initial reading, the 

distance 1-2 thus traveled by the 

tracing point equals the mean height 

of the indicator diagram in inches. 

To prove this, it should first 
l)e mentioned that the motion of 
the wheel corresponding to the 
motion of the point from 1 to 
2 is the same as that corre- 
sponding to the motion of the 
point around the area, since the 
wheel returns backward to its 
initial position during the mo- 
tion 1-2. 

In Fig. 53, the motion 1-2 
of the point causes a change of 
position of the wheel from 5 to 6. 
The line 6-7 is the component of 
this motion which causes roUing of 
the wheel. Since this rolling is the 
same as that taking place when the area is circumscribed, it equals 
M in the formula Mc = area, the area being that of the indicator 




Fig. 53 



15 PLANIMETERS 87 

diagram, and c the length of the planimeter arm (see Test 14, 
principles). Also, 

area = /iXZ 

in which h is the mean height and I the length of the diagram. 

Hence 

Mc 
Mc = hl, from which h = —j-. 

From the similarity of triangles 1-3-4 and 6-7-5, 

-yr =~j J from which S = —j-. 

Hence S = /i, that is the distance 1-2 equals the mean height of 
the indicator diagram. 

(a) Comparison of Records with Known Mean Heights. 
Instead of an indicator diagram, a carefully laid out rectangle 
may be used. The tracing point should be started in the lower 
right-hand corner, and the figure traced back to this starting point. 
The parallel motion necessary to bring the wheel back to its 
initial reading will take the point back to the upper right-hand 
corner of the rectangle, if the instrument indicates correctly. 
This test should be repeated several times, care being taken 
that the point pursues the path of the rectangle closely. 

If the instrument does not indicate correctly, it may be because 
the length of the arm has been altered, through bending of the 
tracing point or otherwise, because of faulty graduations of the 
wheel, or because of the wheel sticking instead of revolving freely. 

Problem 15i. If the length of the arm c is 5 ins., what should be the 
diameter of the wheel so that one revolution corresponds to 10 sq. ins. of area? 

Ans., 0.636 in. 

Problem 152. If the test under (a) gives results uniformly 8 per cent 
too small, is the arm too long or too short, and how much should it be changed 
if its length is 6.12 ins.? Ans., 0.45 in. 

Problem 163. Using the indicator diagram of Problem 148, find the 
mean effective pressures by the Coffin planimeter, and compare results with 
those from the Amsler. 



88 PLAXIMETERS 16 

16. The A^-eragixg of Circular Charts 

Principles. The growing use of autographic instruments of 
precision yielding circular charts has led to the development of 
appropriate methods of averaging and integrating. Recording 
instruments are used both for the measurement of quantities 
which need not be totaled, such as pressures, temperatm^es, CO2 
percentages; and for time rates, such as cubic feet of steam or 
pounds of water per minute. It is often desirable to a\'erage 
such records, and it is essential, in the case of time-rate ones, to 
gei total quantities. The latter may alwaj'S be had, when the 
average rate is known, by multiplying this rate by the time. 
The problem, then, resolves itself into one of finding averages. 

It should be noted, however, that there are available special 
planimeters yielding total quantities from time rate charts, and 
that man}^ recorders are equipped with automatic ones, so arranged 
as to be driven by the same mechanism that moves the chart. 
Averaging methods only will be considered here. 

Circular diagrams always have uniform angular coordinates, 
since they are obtained by clockwork moving in proportion to 
time. The radial coordinates, on the other hand, may be uniform 
or non-uniform, depending upon the law controlling the pen 
movement and its mechanism. When the ordinates are non- 
uniform, the usual methods of averaging do not appl3\ 

(a) The Radial Planimeter. Fig. 54 illustrates the prin- 
ciple of the Bristol-Durand instrument for averaging circular 
charts. This consists of an arm carr\4ng a record wheel and 
tracing point at one end, arranged to slide in a pivoted sleeve. 
With the pivot set at the center of a circular chart, the tracing 
point can traverse an}^ curve on the chart, the arm shding in the 
sleeve when the point moves radially. Since the record wheel 
axis is set on a radial line, the motion of a point on the wheel 
circumference with relation to its axis w^ill be due only .to circum- 
ferential motion of the tracing point. Radial motion of the 



16 



PLANIMETERS 



80 



tracing point will cause no motion of the wheel on its axis. Thus 
it is seen that it is only the circumferential component of the 
motion of the tracing point which causes rolling of the wheel, 
and since the circumferential component is proportional to the 
radius, it follows that the rolling will be proportional to the radius. 




Bc7se Circle 



Fig. 54. — Radial Planimeter. 



To deduce the equation of the instrument, let 

iJ = average distance of tracing point to pivot center = 

average radius of curve, inches ; 
r = distance between tracing point and plane of wheel, 

inches; 
ro = distance between center of chart and zero of circular 

coordinates, inches; 
d = diameter of wheel, inches; 
n = number of turns of wheel when tracing point traverses 

a given curve; 
/= fraction of the time included between the curve limits 

to the time represented by a complete revolution of 

chart; 



90 PLANIMETERS 16 

Then the motion of a point on the wheel circumference will be 

7rdn = 27r{R-r)Xf, 

the quantity on the right being the circumferential component 
of the wheel motion which exclusively produces rolling. Trans- 
posing 

If r is made equal to Tq (adjustment for this is provided), then the 
value oi R — r above is the average radius of the curve in inches, 
measured from the base circle. Multiplying by the scale of 
radial coordinates gives the desired mean. 

If the tracing point is between the wheel and the pivot, the 
equation becomes 

To get the mean height from the base circle, in this case, it is 
necessary to multiply the number of turns, n, by d/2f and subtract 
from their product r and ro. 

Calibration curves can be made for ready use with charts of 
given form. 

When the radial coordinates are curved (that is, produced b}^ 
a pen swing around a center), an error will result if the ends of 
the curve do not join. To obviate this, the tracing point must 
be brought back to the same radial distance from the chart center, 
at the finish as that at the start; and this closing must be made 
by following a curved radial coordinate. 

The instrument may be tested for accuracy, first, by tracing a 
circle of known radius; and, second, by noting whether a wholly 
radial movement of the tracing point rolls the wheel. 

(b) Approximate Average with Integrating Planimeter. This 
instrument is not appropriate to circular diagrams as might at 
first appear. If the area of such a diagram be found with the 



6 FLOW METERS 91 

polar planimeter and divided by its angular measure expressed 
in radians, and the square root of this quotient taken, the result 
will be the square root of the mean of the squares of the radii, 
instead of the arithmetical mean. However, in cases where 
the record is not that of a very variable quantity, these two 
values are not materially different, so that the one can be taken 
in heu of the other. The procedure is as follows : 

Close the gap at the ends of the curve to be averaged by 
radial lines, and then find the area bounded by the curve and the 
radials. Then, if / is the fraction of the time included between 
the radials to that represented by a complete chart revolution, 
the mean height of the curve from the center of the chart is 
(approximately) 



^ /Area 



-/ 

The average quantity in scale units is now found by noting the 
value of a division on the chart at a distance from the center 
equal to this mean height. 

FLUID VELOCITIES— Meters 

Meters for the measurement of fluid quantities are of two 
broad types: those that measure volume or weights directly 
and those that measure velocities. 

Volume meters are so arranged that all of the measured fluid 
passes through them, alternately filling and emptying com- 
partments and thereby displacing a moving part which registers 
through a gear and counter combination, the quantity passed. 
This type of meter gives the total quantity at any time. To 
get rates it is necessary separately to count the time. 

Velocity meters measure quantity by means of the relation 
that the flow in volume units per unit of time is equal to linear 
velocity multiplied by the cross-sectional area of the fluid. Such 



92 FLOW METERS 17 

meters are dependent upon the uniformity of velocity throughout 
the cross-section, or upon the correctness of an estimated average 
velocity when it is not uniform. They may be calibrated to give 
volumes or weights per unit of time. To get total quantities, 
it is necessary to multiply by the time. 

17. Calibration of a Volume Water Meter 

Principles. In some types of water meter, the moving part 
is a piston or disc which is displaced by the water entering the 
compartment of which this moving part is a wall. There may be 
leakage past the moving part or the valve motion which controls 
it. This leakage will increase with the pressure drop through 
the meter. The greater the pressure urging the water through 
the meter, the faster is the flow. Hence, the accuracy of a water 
meter will vary with the rate of flow. Other types of water 
meter, which may be arranged to avoid such leakage, still will 
have variable accuracy owing to the effect of inertia, etc., at 
different rates. For a complete calibration, then, a meter should 
be tested at enough different rates to cover its range. 

(a) Calibration against a Calibrated Tank cr Scales. The 
meter is arranged so that the water passing through it can be 
weighed in a tank placed on a platform scales or measured in 
volume from the known dimensions of the tank. If the volume 
is measured and the instrument reads in pounds, or vice versa, 
it is necessary to know the density of the water with reference 
to its tem])erature. Enough readings of both the true quan- 
tity as shown l^y the scales or tank and of the meter should 
be taken to get fair values of the rates of flow. In this connec- 
tion, rules 4 and 5 given on page 8, should be carefully followed. 
From the observations, should be figured a series of ^^ true rates ^' 
in pounds, gallons, or cubic feet per unit of time, and of *' rates 
by the meter '^ in the same units. If desired, these may be plotted 
for a calibration curve. 



17 FLOW METERS 93 

(b) Curve of Correction Factors. This is more convenient 
to use with a volume meter than a caUbration curve, because the 
instrument is not as a rule used to get rates, but total quantities. 
The correction factor at any rate of flow is that number by which 
the total quantity as shown by the meter for any length of time 
is multiplied to get the true quantity. Consequently, the cor- 
rection factor is the ratio of the true rate to that shown by the 
meter. A series of values of the factor may be calculated from 
the calibration curve and plotted against the rate by the meter. 

In using the curve, to select the appropriate correction factor, 
a rough value of the rate by the meter is figured, and from the 
curve the corresponding factor is obtained. The true quantity 
for the total time is then readily determined. 

Problem 17i. Discuss the following observations taken from the test of 
a meter, and from them figure the true rate, the rate by the meter, and the 
correction factor. 

Time. True Weight. Weight by Meter. 

2:10 50.5 lbs. 10.0 lbs. 

2:15 68.8 20.8 

2:20 80.1 31.5 

2:25 91.3 42.1 

The first true weight is that of an empty tank on a platform scales. 

Ans., 2.25 and 2.13 lbs. per min.; 1.06. 

Problem 172. If a water meter of the volume or displacement type is 
accurate at all rates when the water is 60° F., draw its calibration and correc- 
tion factor curves to be used when the water is at 120° F. (See p. 369.) 

18. Calibration of a Volume Gas Meter 

Principles. The gasometer is the most accurate instrument 
of this t^^pe. It is represented by Fig. 55, and consists of two 
tanks as shown, the upper one being movable vertically and 
properly counterbalanced. This arrangement makes a chamber 
of variable size and water sealed. When the upper tank is raised, 
gas is drawn through the inlet pipe, the valve being closed and / 
open. When lowered, the gas is discharged, the valve control 



94 



FLOW METERS 



18 



being reversed. The volume of gas thus displaced is measured 
by the vertical motion of the upper tank, its cross-section being 
known. 




'6a 6 Pipe-'^ Out In 

Fig. 55. — Gasometer 



It will be noted that the gasometer cannot be used for measure- 
ing continuous flow unless two are operated, one to fill and one 
to discharge, alternately. 

Another form of gasometer is shown by Fig. 56. Gas is drawn 
into the cylindrical chamber C by allowing water to flow out 
through the outlet pipe. This gas is then displaced through the 
gas outlet Ijy causing water to enter through the water inlet, the 
valves being properly adjusted. The gas displaced is measured 
by the rise of water level in the gage glass. 

Commercial forms of gas meter are generally of the '^ dry 
meter ^^ t3'pe and are arranged to measure continuous flow. 
In this type there are two bellows chambers which are alternately 
filled and emptied. One side of each bellows being stationary, 



18 



FLOW METERS 



95 



the other one is thus given a motion which actuates through a 
linkage the valve control and the recording mechanism. 



Gas tnJeh 
.•Manomefer 




Fig. 56. — Gasometer. 



As gas meters in general record volumes under the exist- 
ing conditions of pressure and temperature, these conditions should 
be noted if it is desired to translate the readings into weights 
or into volumes under standard conditions. (See p. 171.) 

(a) Calibration against a Gasometer. The meter to be 
tested is arranged as shown by the dotted lines of Fig. 56. The 
gas used for testing may be air; the gas inlet may then draw 
through an open pipe. The gasometer being full of air, water 
is caused to enter through the water inlet, its rate of flow being 
the desired gas rate. This is obtained by manipulating the water 
inlet and noting the time of rising in the gage glass. The valve 
in the outlet pipe at the meter is then adjusted so as to give a 
constant air pressure as shown by the manometer which, if equal 
to that usual in city gas mains, should be about four inches of 
water. 

For other details, see Test 17 (a). 



96 



FLOW METERS 



19 



(b) Curve of Correction Factors is obtained the same as for 
a water meter, Test 17 (6). 

Problem 18i. In calibrating a gas meter the capacity of which is 500 
cu. ft. per hour, what rates should be appHed, and how long should each trial 
be so that the error due to reading the gage glass is no more than 1 per cent? 
The diameter of the gasometer is 3 ft. 

Problem I82. What should be the capacity of a gasometer to calibrate 
a meter of 2000 cu. ft. per hour capacity? 



19. Calibration of a Weir 



Principles. A weir is a water meter of the velocity type. It 
is formed by a notch made in a dam like obstruction in a stream 
of water through which notch all of the water is caused to flow. 
The level of the water behind the dam stands above the bottom 
edge or sill of the notch, and according to a definite difference 
in these levels, a definite velocity is attained by the water, and 
hence the quantity passed in a unit of time. If it is arranged 
that the difference of level be measured by a precise instrument, 
such as a hook gage, then the flow may be calculated; or, if the 

weir has been calibrated, the flow may be 
obtained from the calibration curve. 

Fig. 57 shows a weir, the height of the 
water level above the sill being represented 
by H. The pressure to which the particles 
of water at the sill are subjected is equal 
to // ft. of water. W^hen this pressure is 
reduced to zero by emergence of the water 
into the atmosphere, the work done is WH 
ft.-lbs. per second, W being the weight of 
w^ater in pounds per second. This work 
is transformed into kinetic energy, the 

Try2 

expression for which is — — , V being the 




Fig. 57. 
Weir and Hook Gage. 



19 FLOW METERS 97 

velocity in feet per second, and g the acceleration of gravity. 
Consequently, WH = WV^/2g and, 

The velocity of the particles of water at levels above the sill is 
less than this since they are at less pressure, and it may be shown 
that the average velocity is f F or f X v 2gH, If the breadth of the 
weir is B ft., then the cross-sectional area to which this average 
velocity applies under ideal conditions is BH sq. ft. Then, since 

Quantity = area X velocity, 



it follows Q' = BH Xl^2gH 

= lBV2gIP, 
Q' being in cubic feet per second. 

This is for ideal conditions. Actually, the velocity is some- 
what less than the ideal because of eddies and friction of which 
the theory takes no account. So we may write 

Actual velocity = CiX ideal velocity. 

Ci is less than unity and is called the ^^ coefficient of velocity." 
Also the actual water section is less than BH since there 
is generally a contraction due to a fall at the top and a narrowing 
at the edges of the weir on account of the tendency of the water 
at the sides to continue in the plane of the weir. Hence, 

Actual area = C2 X BH 
in which C2 is the '' coefficient of contraction." 



Mi 



98 FLOW METERS 19 

It follows that the actual quantity 



Q = iCiC2BV2gH\ 

C being called the ^' coefficient of discharge/' 

For rectangular weirs with sharp edges, C equale about 0.62, 
depending upon the size of the weir and the head. 

When the stream behind the weir is small in cross-section, 
its velocity is relatively high. The so-called velocity of approach 
will then appreciably increase the velocity of the water through 
the weir since it acts in addition to gravity, and should be allowed 
for. The average velocity of approach may be calculated by 
multiplying the velocity through the weir by the ratio of water 
sections at the weir and in the flume behind the weir. The 
additional head urging the water through the weir is then 

(Velocity of ap proach ) ^ 

which may be added to H for use in the formula for Q. This is 
an approximation since the velocity in the flume is very variable 
throughout the cross-section. The actual velocity of approach 
is greater since the water in the middle of the stream, having 
greatest influence on the passage through the weir, is of higher 
velocity than at the sides and bottom. It is more correct, then, 
to multiply the velocity head as just given by a number greater 
than unity which, according to Hamilton Smith, lies between 
1.0 and 1.5. 

Many modifled formulas have been proposed for weirs to 
allow for the variations of C2 and C. The most notable, perhaps, 
is Francis^ 

Q = 3.33 {B-0.2H)V]p^ 



19 FLOW METERS 99 

in which 3.33 equals C iV2g. In this, it is regarded that each 
end contraction increases with the head and equals O.IH. There 
is thus less variation in the applied value of C which remains 
approximately equal to 0.62. This formula may be used for 
uncalibrated weirs having B greater than 4 ft. when the head, //, 
exceeds 5 ins. ; wath less than 1 per cent of error. 

Other shapes of weir notches are the V-notch and the trape- 
zoidal. For the former the equation is 



Q = C^,V2gH' 

when the sides of the notch make a right angle. See Test 20. 

There is less variation in the coefficient of contraction for this 
type of weir than the rectangular. Also it is useful for variable 
flow and small quantities since the head diminishes at a rapidly 
decreasing rate with the quantity. 

Merriman recommends an average value of C, 0.592, which 
gives 

Q = 2.5W1p, 

F-notch weirs are now made with elaborate indicating and 
recording apparatus to register the flow. (See Test 20.) 

The trapezoidal weir may be arranged so that the extra breadth 
due to the slope of the sides as the head rises balances the increased 
contraction of section so that the product of the breadth B at 
the sill and the coefficient of contraction remains nearly constant. 
The slope of the sides should then be 1 to 4. The value of C 
may be taken as 0.62, and we have, as for a rectangular weir 
without end contractions, 

Q = 3.33BV1p. 

The difference of level, H, is generally measured by the hook 
gage, Fig. 57, by which minute differences of level may be detected. 



100 FLOW METERS 19 

In use, the hook is started just below the water level, then raised 
slowly until it barely breaks the water surface, fastened in that 
position and then read at the graduated scale. 

(a) The Zaro of the Hook Gage is its reading at a given 
datum plane. For a weir, this plane is the horizontal one through 
the lowest edge of the notch. To get the zero of the hook gage 
for a weir, a straightedge should be placed with one end at the 
lowest point of the notch and the other end on the point of the 
hook, and so balanced that very little weight comes on the hook, 
to prevent springing it. The hook is then raised or lowered until 
a spirit-level placed on the straightedge show^s the horizontal, 
and a reading taken. The straightedge and level are then turned 
end for end and the procedure repeated. By averaging the two 
readings, any untruth of the straightedge or level is eliminated. 

(b) To Calibrate a Weir, a series of readings of head and 
corresponding quantity rates in cubic feet per minute or second 
should be obtained and plotted. To get the quantity rate, the 
water may be discharged into a calibrated tank, the rate of rising 
in which will give the volume per minute. When the weir is at the 
end of a flume of uniform horizontal cross-section, a convenient 
method is to start with it empty, and then adjust the incoming 
water to the desired rate of flow. The rate can be ascertained as 
the flume is filling by readings of the hook gage taken at equal in- 
crements of time. When the water level has reached its highest 
position, uniform flow through the weir being established, a 
final reading of the hook gage gives the head corresponding to 
the rate thus previously ascertained. With this method, it is 
especially important that the rate be constant toward the end 
of each run. 

(c) The Coefficient of Discharge varies with the rate. For 
any rate, it may be found from the quantity formula, the values 
of // and Q being known. 

Problem 19i. Find the coefficient of discharge from the following experi- 
mental data obtained from a rectangular weir. Size of flume 18 ft. long 



20 



FLOW METERS 



101 



by 3 ft. wide. Kate of rise, 0.12 ft. in 5 sec. Head on the weir, 5 ins. 
Breadth of weir, 18 ins. Arts., 0.6. 

20. Calibration of a V-notch Recorder 

Principles. This instrument, largely used for measuring 
boiler feed, is illustrated diagrammatically by Fig. 58. A float 



• Recorder Drum 



'PenCarnaq^e 



PJcfte Cam 




Fig. 58. — Principle of Cochrane V-notch Reccrder. 

is situated in a weir tank in such a way as to be in a quiet level. 
A vertical spindle on the float communicates the rise and fall of 
the water to a plate cam by means of a steel cable wound around 
a drum on the cam shaft. As the cam revolves, it engages a pin 
on a carriage so as to move the carriage from left to right according 
to the height of the float, and, therefore, the rate of flow. The 



1 



102 FLOW METERS 20 

cam groove is a polar curve having the equation of flow; conse- 
quently the motion of the carriage is directly proportional to the 
flow and not to the head causing the flow. The carriage carries a 
pen which records on a drum chart. 

The Lea V-notch recorder is much the same in general prin- 
ciple, but a cylindrical cam is used. Another type of V-notch 
recorder makes use of a specially shaped weighing float, the 
vertical motion of which is proportional to the rate of flow. 

The equation cited under Test 19 for a 90° notch isQ = 2.53V IP 
in which Q is in cubic feet per second, and H is in feet. If h is 
the head in inches, and q the cubic feet per minute, then 

g = 3.04\/p. 

These meters are generally graduated to read in pounds, 
in which case there may be an error because of change of density 
of the water. This error is partly compensated for, in that, at 
a higher temperature, for a given head, a lesser weight of water 
will pass, but, on the other hand, the float will stand lower in 
the hot water, thus making the recording pen indicate less. If 
the flow were proportional to the head, the correction would be 
exact. 

(a) Zero Level of Weir. Some forms of these meters are 
provided with an inside and outside pointer indicating this level, 
the outside one being adjustable. If there is none, the hook 
gage can be set as described under Test 19, if convenient. 
When the hook gage, with which the calibration is to be made, is 
outside the weir tank (it is often located in a vertical pipe con- 
nected at the bottom with the tank, for convenience in handling, 
and securing still water), the following procedure may be used. 

The weir is blanked off with some boards, as indicated by Fig. 
59. A gage, <;, of a convenient height, say 1 in., is set in the 
weir as indicated. The water level should now be brought to the 
point of this gage, and a reading of the hook gage taken. The 
zero level of the weir is then 1 in. below this reading. 



20 



FLOW METERS 



103 



(b) Calibration. Since the coefRcient in the formula 
q = 3.04:\/H^ is very well established, and is practically con- 
stant under usual operation (ranging about 1 per cent above 
and below), this formula furnishes a ready means of calibra- 




FiG. 59. — Gage Pointer for Finding Zero Level. 



tion. It is only necessary to measure the head corresponding 
to any instrument record, and from this calculate the actual 
flow. The mechanism should first be set to register zero when 
under a zero head as located by method outlined in (a). Note, 
that the height of the float should not be used for obtaining heads. 
Temperatures should be taken to enable the calculation of the 
flow in pounds. 

The coeflficient, 3.04, applies to a 90° notch. 54° notches 
also are used. This angle gives half the area of the right-angle 
notch. The coeflficient is a little greater than half that of the 
latter, and may be taken equal to 1.55. 

(c) Sensitiveness. With the hook gage set at a convenient 
height, start with a low level behind the weir, and gradually 
increase it until the gage is just submerged. At this instant a 
reading of the recorder should be noted. The procedure should 
be repeated, the hook gage position unchanged, with the head 



104 



FLOW IMETERS 



21 



decreasing. The difference between the readings represents 
twice the lag due to friction of the recording mechanism. 

21. Calibration of a Nozzle 

Principles. A nozzle makes a very convenient form of velocity 

water meter when the water to be 
measured may be discharged from a 
pipe into the atmosphere. The prin- 
ciple upon which this meter depends 
is similar to that of a weir, that for a 
definite pressure behind the opening 
there will be a definite flow through it. 
Then, if it is arranged that this pressure 
be measured, the flow may be ascer- 
tained in cubic feet or pounds per unit 
of time either by calculation or from a 
calibration curve. 

The equation of a nozzle ma}^ be 
obtained from a consideration of the 
energy appearing in the water. In Fig. 60 the energy at 
the section a is in two forms, pressure and velocit3% neglect- 
ing the small amount of potential energy due to the height 
at a above the opening at 6. All the energy at a is 
converted into velocity at 6, since the pressure at h is nil, 
except that used to overcome fluid friction between the points 
a and h. Let W equal the weight of water passing per second. 

Then the available energy at a is WH+— — , H being the pres- 

sure in feet of water and V the velocity in feet per second at a. 

The expression ^ is the kinetic energy at a, and WH the 




Fig. 60.— Nozzle. 



2^ 
pressure energy. Likewise, the energy delivered at h is 



23' 



21 FLOW METERS 105 

If vi is the velocity at b under the ideal condition of no losses, 
then 

in which C is a coefficient less than unity. Since energy is propor- 
tional to the square of the velocity, 

C^X available energy = delivered energy. 

Substituting in this the values of the energies as previously 
noted, 

We also have the relation that the velocities are inversely propor- 
tional to the cross-sectional areas, or 

V_ 4 ^rf2 
i;~7rZ)2~Z)2- 



Combining these last two equations we have 






Since the quantity, Q, in cubic feet per second, equals the velocity 
times the area of the stream, 



Q = 0.7854d2^^?fg. 



..^^ 



106 FLOW METERS 21 

For convenience, this may be expressed 

Q = 6.3C , Vg, 

in which JS is the ratio of D to d. Note that the units of D are 
feet. 

The value of C for a well-designed nozzle is between 0.95 and 
0.99. It is thus seen that such a nozzle may be used as a meter 
without material error if it is uncalibrated. 

A convenient method of measuring the pressure is by a mer- 
cury manometer as shown in Fig. 60. The difference in level of 

the mercury in inches should then be multiplied by -^ to con- 

vert into feet of water. The lower level of mercury should be 
referred to the datum plane through the end of the nozzle (when 
the nozzle is vertical) as this allows for the potential energy 
between the sections a and h which was neglected in the formula; 
the column of water in the right-hand leg of the manometer balanc- 
ing that within the nozzle. If the mercury descends below the 
datum plane, the reading of the manometer must be corrected 
for the head of water between the lower mercury level and 
the datum. When the nozzle is horizontal, the datum plane 
should be through the axis of the nozzle. 

(a) Calibration at Various Rates. The rate may be varied 
by turning a stop valve in the pipe to which the nozzle is affixed, 
and the rate may be measured by discharging the water into a 
calibrated tank or by weighing it. If the pressure measuring 
device is a manometer, the tube connecting it with the nozzle 
should be full of water as any air in it will cause the apparent 
water head to be different from the actual by amounts varying 
with the pressure. The water head below the datum plane 
may be corrected for by translating it from inches of water to 



21 FLOW METERS 107 

inches of mercury and subtracting from the manometer read- 
ing; or the manometer may be raised each time it is read 
so that the lower mercury level is at the datum plane at 
the instant of reading. The determinations of rate in the 
desired units should be plotted against pressures in inches of 
mercury. 

Rules 4 and 5, page 8, should be carefully observed. 

(b) The Coefficient of Discharge varies somewhat with the 
rate, at any value of which it may be found from the quantity 
formula, the values of H and Q and the diameters of the nozzle 
being known. 

Problem 21i. What is the discharge in cubic feet per second from a nozzle 
having a diameter ratio of 2 to 1, the smaller diameter being \ inch, if the 
manometer shows 5 ins. of mercury with its lower level 7 ins. below the 
nozzle mouth? Assume C = 0.97. Ans.y 0.0246 cu. ft. per sec. 

Problem 2I2. Assuming that a nozzle has been caUbrated with water at 
60°, will more or less water (weight and volume) emerge for a given reading 
of the U-tube when the water is at 120°? Why? 



22. Calibkation of a Venturi Meter for Water 

Principles. The Venturi meter is similar in principle to the 
nozzle. It is, in fact, a nozzle discharging into a closed and 
properly shaped pipe instead of into the atmosphere. See Fig. 
61. The water passing through the pipe shown carries a certain 
amount of energy in the form of pressure and velocity. When 
the water reaches the contracted section 6, its velocity is increased, 
and therefore its pressure must be decreased, since the total 
energy, barring losses, remains constant. The drop in pressure 
between sections a and h thus becomes a measure of velocity 
and hence quantity. 

To deduce the equation for the Venturi meter it is only 
necessary to equate the expressions for energy at the two sec- 



108 



FLOW METERS 



22 



•Dia. ' D 







tions a and h. Thus, if V and y are the velocities in feet per 

second, and H and h the 
pressures in feet of water 
at the sections a and 6, 
respectively, and W the 
weight of water passing 
per second, then 



g being the acceleration of gravity. We 
also have the relation 

7 _ Area at b_ dP 
V Area at a D^' 

Combining these equations and solving 
for Vj 




Fig. 61. — Venturi Meter. 



from which the cubic feet per second discharged under ideal 
conditions is 

Q' = area X velocity 

Owing to friction losses the discharge thus calculated is too high. 
To allow for this, a coefficient of discharge, C, less than unity, 
is introduced. Combining V 2^ and 0.7854, for convenience, the 

formula becomes 

7)2 ^ 

Q = 6.3C . VIT^ 

in which R is the ratio of D to rf, and D is in feet. 

The value of C for a well designed Venturi meter is between 



^ 



22 



FLOW METERS 



109 




0.95 and 0.99, and the value of R is usually 2 or 3 to 1. It is thus 
seen that an uncalibrated Venturi meter may be used with not 
more than 2 per cent of error by assuming C = 0.97. 

The meter is generally shaped with an annular space A, Fig. 
62, from which to lead the opening transmitting pressure. Be- 
tween this annular space, or pressure cham- 
ber, and the interior of the tube are circular 
openings connecting the two. This arrange- 
ment transmits the pressure more truly 
than would a single opening. 

For measuring the difference of pressure, 
H-h, a mercury manometer is generally 
used connected as shown by Fig. 61. When 
the manometer is graduated in inches, the 
flow may be calculated or obtained from 
a calibration curve determined experiment- 
ally. The manometer is sometimes gradu- 
ated in quantity rates so that no curve 
need be used. 

Some forms of Venturi meter employ apparatus giving a 
continuous record on a time chart which, when integrated, 
yivjlds total quantities. One of these is illustrated by Fig. 63. 
Note the cam by which movement of the mercury column (pro- 
portional to the square of the velocity), is rectified to give 
uniform radial chart ordinates. 

(a) The Calibration at Various Rates may be made by con- 
trolling the rate by a stop valve in the water line and measuring 
the rate by discharging the water into a calibrated tank or by 
weighing it. A curve should be drawn between the rates and the 
differences of mercury level (manometer readings). 

Rules 3, 4 and 5, page 8, should be carefully observed. 

(b) The Coefficient of Discharge is determined from the 
formula at any rate when the values of Q, iJ-/i, and the diameters 
of the instrument are known. 



Fig. 62. 



no 



FLOW METERS 



22 



The head in inches of mercury should be transposed to feet 
of water. Referring to Fig. 61, it is seen that the column of water 
on the right above X balances an equal column on the left. The 



. (-Metal Disc for Chart 

— Capillary ?en 

Ten Arm 

a Pay Clock- 
in Metal Case 

•Aluminum Vise 

Counter Dial f late 

J iiuj I > i I ,u ■ Counier Dial 

4Day Integrating Clock- ^ ' " " ^ ^' " " '^" ^ 

Aluminum Yoke -^v.-.VV~^n / \ /X" Indkahr Dial hand 

CamRoller "'' /) v ^ J A^fA Indicaf or dial 'Removed 

Support ior Indicafordiol-- 

ZeroUne-- — -- 

Cam-- — " 

Main Shaft 



Main Levari 
From Float/ 




--Case 



Fig. 63. — Builder's Iron Foundry Venturi Meter Recorder. 



column of water between X and F, however, is balanced by 
mercury, so that the pressure difference between sections a and 
b is not XF inches of mercury, but XY inches of mercury minus XY 
inches of water; that is 

(^^'^-^) XY=1,05 XY, feet of water. 



23 FLOW METERS 111 

Problem 22i. Given the diameter ratio 3:1; smaller diameter, 1 inch; 
find the constants Ki and K2 in the following equations: 

q^k.cVhI 

Lbs. per sec. =K2C\^Hi 

in which Hi is the difference of level in the mercury manometer in inches. 
Problem 222. Draw the calibration for the meter of Problem 22i, assuming 
that C = 1, up to a value of Hi = 6 ins. 

23. Calibration of a Venturi Meter for Gas 

Principles. The deduction of the flow formula differs from 
that for water on account of the fact that gas carries intrinsic 
energy due to its expansive property which must be accounted 
for in the equation of energy. Otherwise the principle of the 
deduction is the same. The flow formula has been presented 
by Mr. E. P. Coleman in a paper to be found in the transactions 
of the A.S.M.E., Vol. 28, page 483. The general arrangement 
of the instrument is the same as for water. It has not been 
extensively used for gases probably because the Pitot tube (see 
Test 24) answers the same purpose more cheaply, is considerably 
smaller, and has been more developed experimentally. Never- 
theless, there are obtainable and in successful use recording 
Venturi meters in large sizes for the measurement of gases and 
steam. One of these is similar to Fig. 63. To convert the 
records into standard cubic feet, corrections for both pressure 
and temperature must be appHed. 

(a) Calibration at Various Rates may be accompHshed by 
using one of the methods described under Tests 25, 27, 28, or 
29 for measuring the true quantity of gas; or if the Venturi meter 
is of small size, by using a gasometer. The rates may be obtained 
in cubic feet per second or minute, and plotted against difference 
of pressure in inches of water or mercury. Note that the tem- 
perature conditions must not materially vary from those in use, 
since a change of temperature is accompanied by a change of 
flow. 



112 



FLOW METERS 



24 



24. Calibration of a Pitot Meter for Water 



Principles, 



t 



Fig. 64 represents a Pitot meter, which is merely 
a curved tube placed in a stream of velocity 
V feet per second so that the immersed end 
of the tube faces the stream. The kinetic 
energy of a given weight of the water, W, is 
IFF2/2gr, in which V^/2g is called the " velocity 



rr^^^rir^ head '' or the head of water, H, in feet, 



which under ideal conditions may produce 
a velocity, V. In the Pitot tube, Fig. 64, the 
water rises until the head in the tube just 
balances the velocity head of the stream. Hence 



Fig. 64. 
Pitot Tube. 



V = V2gH, 

The height H thus becomes a measure of velocity and therefore 
quantity. 

If the stream is in a closed conduit, the water may be under 
a pressure greater than atmospheric which would cause it to 
rise in the Pitot tube to a height greater than that due to velocity. 
This may be allowed for by making a separate measurement 
of pressure. Thus, in Fig. 65, H2 ft. of water balances veloc- 
ity plus pressure, and Hi ft. in the 
straight tube is due to pressure only 
owing to the fact that the velocity 
is not impressed upon this tube 
opening. The velocity is then 



V = V2g{H2-Hi), 



The Pitot tube opening is called L T VwIE^V." III*. 




velocity opening 



and 



the 



the '' 

other, the ** static opening.'' They 
are often connected to a differential 
gage as shown by the dotted lines of 



Fig. 65.— Pitot Meter. 



24 



FLOW METERS 



113 



Fig. 65 so that the pressure is balanced, and a single reading 
gives the velocity head direct. 

The plane of the static opening should be parallel to the 
stream; for, if it is inclined toward it, the velocity is partially 
impressed; or, if away from it, suction will result. With a 
correct static opening there m.ay be the same effects if the stream 
is not parallel to the pipe direction, which may be the case at 
points near bends or elbows, or when the instrument itself inter- 
feres with the regularity of the flow. Generally two static open- 
ings on diameters at right angles, connected together, are used. 

When the Pitot tube and static opening are properly designed 
and applied, the actual condition of flow is the same as that 
represented by the formula, so that there need be no coefficient 
to determine as with tlie nozzle, weir, and Venturi meters. 

In a closed conduit, the velocity of the stream varies through 
the cross-section, being maximum at the center and minimum 
at the sides. It is therefore necessary either to find the velocity 
at enough points to get a fair average or to read the instrument 
at a point of mean velocity. The mean velocity is approximately 
0.83 X velocity at center, and this rule is 

.. , « , ,, station Nq 

sometimes used for rough results. y<^^^^^"::l 

(a) Determination of Average Velocity /Zv^^^^^xv^"^ 

and of Quantity Rates by Traversing. r/u /^^^\ uTi^ 

. r'rrrl*''s //III 

In Fig. 66, the concentric circles mark \\\\^^ 

off equal areas so that ai = a2 = as = a4 = 05, \^^^^^/:il 

the area of the pipe being A = 5gi. The ^^^.^sa^^- — 10 

average velocities in these areas are vi, Fig. 66. 

1^2, i'3, etc., respectively, the average veloc- 
ity in the whole pipe section being V. Then, if Q represents 
the cubic feet per second, 

Q = AV = aiVi+a2V2+asvs+etc., 
= 5aiV = ai{vi+V2+vs+etc.)j 
and y^ vi+V2+V3+etc. ^ 

5 



114 



FLOW METERS 



24 



That is, the average velocity in the pipe is the average of veloc- 
ities taken at points representing equal areas. 

The method to be pursued, then, is to take readings of the 
differential gage at such points for a single determination of 
quantity, the quantity being calculated by taking the product 
of the average velocity, F, and the area of the pipe. It is cus- 
tomary to take readings at ten points, or stations, as shown by 
I'ig. 66. The readings on one side of the pipe center should 
duplicate those on the other, and there are two readings for 
each area. The stations should be located at the following 
distances from the pipe wall, D being the diameter of the pipe, 
in order to represent equal areas. 



station No. 1, 


.0256D 


No. 6, 


.658D 


No. 2. 


.08171) 


No. 7, 


.7741) 


No. 3, 


.146D 


No. 8, 


.854D 


No. 4, 


.226D 


No. 9, 


.918D 


No. 5, 


.342D 


No. 10, 


.974D 



The calculation for V is simplified by taking the average 
of the square roots of the differential gage readings, and using 
this in the velocity formula for V//. Note that the head of the 
gage liquid should be converted into equivalent head of water 
in feet. If mercury is used as the gaging liquid, this may h 
done as described under Test 22 (6). If some other Hquid, ai 
oil, is used, its specific gravity should be taken into accoun 
according to the same principle. The quantity rate can b 
expressed as 

Q = a constant X 2 v^'gage reading 



for the simplification of numerical work. 

Recording Pitot meters in various forms are in considerabh 
use, and of these a good example is that of the General Electri( 
Co., appHcable also to steam and gas flow (see page 128). Thes( 



24 FLOW METERS 115 

instruments are calibrated with the velocity opening at a fixed 
position in the stream, and yield charted results in terms of 
pounds, gallons and cubic feet per unit of time. 

(b) Location of the Point of Mean Velocity. If the pipe is 
traversed and the average of the square roots of the gage readings 
obtained as under (a), then the square of this average represents 
the gage reading at the point of mean velocity. This point may 
then be located by plotting on a chart gage readings against 
distances from the wall of the pipe; the distance corresponding 
to the square of the average square root of the gage readings 
being then taken from the chart. 

The location may be found without plotting a curve by 
searching with the Pitot tube for the point at which is registered 
the gage reading as calculated above and then measuring the 
distance of the velocity opening from the pipe wall. If this is 
done, a center reading should be taken when making the traverse 
by which the uniformity of flow may be checked when the search- 
ing is done. 

Problem 24i. Deduce the values given in the table under (a) for the dis- 
tances of the stations from the pipe wall. 

Problem 242. Give a rough value of the quantity rate in cubic feet per 
minute in a 10-in. pipe (internal diameter = 10.02 in.) if the differential gage 
reading at the center is 26 ins. of oil the specific gravity of which is 0.9, an 
inverted U-tube being used. Ans.y 102 cu. ft. per min. 

Problem 243. Figure the constant for use in the quantity formula for 
an 8-in. pipe (internal diameter = 7.98 ins.), the gaging hquid being mercury. 

Ana.y .285, in cu. ft. per sec. for 10 stations. 

Problem 244. Figure the cubic feet per second in an 8-in. pipe (internal 
diameter = 7.98 ins.) if a traverse gives the readings, 1.02, 1.26, 1.42, 1.56, 
1.69, 1.65, 1.5, 1.38, 1.25, 1.01 inches of mercury. Ans., 3.32 cu. ft. per sec. 



25. Constants of a Pitot Meter for Gas 

Principles. The Pitot meter may be used for gas exactly 
the same as for water (see Test 24) except that greater precau- 
tions should be taken on account of the fact that gas is a much 



116 



FLOW METERS 



25 



M 



<- 



1". 



more mobile fluid. The instrument should be placed at a 
distance of at least 12 pipe diameters from the nearest bend 

on the up-stream side, and four on 
the down-stream. A Pi tot tube of 
unusual proportions or design should 
not be used without previous calibra- 
tion, as it has been found by experi- 
ment that apparently unimportant 
details cause large errors in the indi- 
cations. The best proportions of 
Pitot meter for gas under general 
conditions have not yet been satisfactorily established, but 
Fig. 67 represents the form recommended by the American 
Society of Mechanical Engineers. Numerous experiments, how- 
ever, lead to the conclusion that it is sufficient to have two 
static openings at the wall of the pipe, instead of as shown by 
Fig. 67.* 

In the case of gas, in the formula 



y "^-i -0.02" Ho 1 65 

'•Static Tube, ky I'ci- 
"'Velocity Tube. ^' Diet. 

Fig. 67.— Pitot Tube for Air. 



V = V2gH, 

H is the head due to velocity" expressed in feet of whatever gas is 
flowing, allowing for its density due to its condition of pressure 
and temperature. The observed head in terms of inches of the 
gaging liquid must therefore be translated. For this purpose 
the following relation may be used, 

Tj_h density of gaging liquid 
12 density of gas in pipe ' 

in which h is the observed head in the U-tube connected as shown 
in Fig. 65, expressed in inches. The densities are generally 
given in pounds per cubic foot. Water is usually used for the 
gaging liquid, the density of which may be taken as 62.3 lbs., 



♦ See work of Wm. Rawse, Vol. 35, Trans. A.S.M.E. 



25 FLOW METERS 117 

as it varies but little with temperature.' Kerosene is also used. 
Its density may be figured from its specific gravity. 

(a) Determination of Average Velocity and of Quantity 
Rate by Traversing. The experimental procedure is exactly 
the same as for Test 24 (a) when the gas is at room conditions of 
temperature and pressure, that is, approximately 70° F., and 14.7 
lbs. Air, for example, under these conditions weighs .0749 lb. 
per cubic feet, so 

/IX62.3 
^=12^<:07r9 = ^^-^^^ 



from which 



V = V2g(mM) =m.7Vh, 



in which h is the observed head in inches of water. 

At other pressures and temperatures, the density varies 
according to the relation (for perfect gases) 



144 
U4:pv = p~^ = RT, 

w 



in which p = absolute pressure in pounds per square inch; 

?; = specific volume in cubic feet per pound; 

u' = density, in pounds per cubic foot; 

i2 = 53.4, for air; 

7 = absolute temperature, degrees F. 
From this relation, follows 

144p 

Now 



V = V2yH = yJ2g^X 



62.3 

w 



118 FLOW METERS 25 

Substituting the value of w and simplifying, 



="-^Vf^ 



P 

from which the quantity, Q, in cubic feet per second, may be 
figured b}^ multiplying by the area of the conduit. 

If the quantity rate, in pounds per second, W, is wished, the 
following may be used: 



W = wQ = '^X.7S5i^xn.l 



4'- 

in which (i = diameter of conduit in inches. Simplifying, 



TF = .163d2^^|. 

The absolute temperature is figured by adding 460° to the tem- 
perature as obtained by a Fahrenheit thermometer. For the 
absolute pressure of the gas, p, the barometer should be read and 
added in the same units to the static pressure of the gas as shown 
by a L'-tube or other pressure gage. This gage may be con- 
nected to the static opening of the Pitot meter. 

For any other gas than air, or for any other gaging liquid 
than water, an equation may be deduced similar to the above 
by the same method. 

The procedure, then, for gas at temperatures and pressures 
materially different from room conditions is either 

Firstj to make a traverse from which the average of the square 
roots of the differential gage readings yields V^, and to get one 
set of readings of temperature, static pressure, and barometer. 

Secondy to place the Pitot tube at a point of average velocity, 
by which h is obtained by a single reading, other measurements 
the same. 



26 FLOW METERS 119 

(b) The Location of the Point of Mean Velocity may be 
found exactly the same as for water, Test 24 (6) . 

Problem 25i. What is the velocity, cu. ft. per second, and pounds per 
second of flow of illuminating gas in a 3-in. pipe (internal diameter = 3.07 
ins.) if the reading of the differential gage is 1.5 ins. of oil of specific gravity 
0.85? Pressure of the gas is 4 ins. of water; barometer, 29.7 ins. mercury; 
temperature 55° F. R, for this gas, is 60.7. Ans.y 0.276 lb. per sec. 

Problem 252. Figure the constant in a formula like F = 66.7V/i, to apply 
to Problem 25i. Take average conditions to be 14.7 lbs. absolute pressure 
and 60° F. Ans., 65.8. 

Problem 253. What is the velocity in feet per second if /i = 12 ins. of water, 
pressure =4 ins. of mercury, temperature = 120° F., barometer = 30.1 ins. 
of mercury, the gas being air. Figure answer by both approximate and 
accurate formulas. Ans., 231 and 226 ft. per sec. 



26. Calibration of an Orifice for Water 

Principles. If water is caused to pass through an orifice, 
the pressure behind the orifice being measured, the flow may be 
calculated. Suppose that the velocity of the water behind the 
orifice is negligibly small; then the energy available is WH, W 
being in pounds per second, and Hj the pressure in feet of water. 
This pressure energy is expended in imparting velocity, or kinetic 
energy, to the water upon passing through the orifice, so that, 
neglecting friction, etc., WH = WV''^/2g, F' being the velocity 
in feet per second, and g the acceleration of gravity. Hence, 
under ideal conditions, V = \^2gH, Owing to friction losses, the 
actual velocity is somewhat less than this, so that if ci is a number 
less than one, 

V = ciV2gH. 

If we multiply this by the cross-sectional area of the stream, we 
shall get the quantity, Q, in cubic feet per second. Now, this 
area is less than that of the orifice; the stream being contracted 



120 FLOW METERS 26 

by virtue of the tendency of the water particles to flow in the 
plane of the orifice ; so that if co is a number less than one, 

area of stream = C2X. 7854 d^, 

the orifice being circular and d ft. in diameter. It follows that 

Q = ciC2X.7854dV2ffi/ 
= cX.78o4:dW2gH. 

ciy C2, and c are called the '^ coefficients of velocity, contraction, 
and discharge, '' respectively. Merriman gives average values for 
them as .98, .62, and .61 for the case of orifices with sharp edges, 
that is, orifices in thin plates beveled on the side not touched by 
the water, so that the water touches only one line of the orifice. 

The coefficients vary with the head and with the diameter 
of the orifice. 

In order that the velocity back of the orifice shall be negligible, 
the cross-section of the stream in the conduit should be at least 
one hundred times that of the orifice. If the water conduit is 
round, this means its diameter should be at least ten tinies that 
of the orifice. 

The pressure back of the orifice may be measured by a mercury 
manometer or by a Bourdon gage, or the actual height of water 
above the orifice may be measured direct with a gage glass, float, 
or hook gage (see p. 96). 

As with a rectangular weir, the coefficients vary considerably 
with both the head and the size of the opening. The average 
value, c = .61, should therefore be taken only for rough results. 

The coefficient of contraction varies with the shape of the 
orifice, one having edges rounded toward the inside giving 
markedly less contraction. 

(a) Determination of Quantity Rates at Various Heads 
may be made by discharging the water into a weighing tank, 



26 FLOW METERS 121 

or by measuring its volume. The quantity discharged in cubic 
feet per minute should be plotted against the head in the observed 
units. 

(b) Determination of Coefficients. The value of c may be 
calculated from the formula when the values of Q, H, and d are 
known. The coefficient of contraction may be found by measur- 
ing the diameter of the stream at the contracted section with a 
cahper, this section being distant from the plane of the orifice 
by about a half diameter. Knowing this coefficient, and the 
coefficient of discharge, the coefficient of velocity is readily 
obtained. 

Problem 26i. What is the coefficient of discharge, if an orifice discharges 
92 lbs. of water per minute under a pressure of 3 lbs. per square inch? 
Diameter of the orifice is 0.6 in. Ans., 0.594. 

Problem 262. If the diameter of the contracted section (see Problem 
24i) is 0.36 in., what are the coefficients of contraction and velocity? 

Arts., 0.6; 0.99. 

27. Calibration of an Orifice for Gas 

Principles. The deduction of the flow formula differs from 
that for water on account of the fact that gas carries intrinsic 
energy due to its expansive property, which must be accounted 
for in the equation of energy. The theoretically correct flow 
formula is deduced in various works on thermodynamics. It 
includes necessarily a coefficient c to allow for contraction and 
losses, as is the case with water passing through an orifice. For 
gas, however, the value of c is very uncertain, especially for high 
pressures, there being insufficient experimental data on this 
quantity. 

When the pressure drop between the two sides of the orifice 
is small, the volume of the gas changes but little, and consequently 
only little intrinsic energy is delivered to influence the flow. 
Under these circumstances, the intrinsic energy may be ignored, 
and an equation deduced similar to that for water (Test 62, 



122 FLOW METERS 27 

principles), namely V = c\/2gH, the head, H^ then being the 
height of a column of gas to produce the pressure drop, its density 
being taken into account. 

Since the orifice generally may be designed of such size to 
produce a small pressure drop, it seems hardly worth while to 
use the accurate and much more complex formula, especially 
in view of the uncertainty of the v^alues of the coefficient of 
discharge under those conditions to which the hydraulic formula 
does not apply. 

The gas may be caused to flow into the atmosphere, in which 
case, the pressure drop equals the pressure of the gas above 
atmosphere, and may be read by a manometer. If the gas can- 
not be discharged in this way, the orifice may be in a plate fitting 
square across the gas conduit, and the drop of pressure measured 
with a differential gage as with the Venturi meter, Fig. 61, except 
that water should be used as a gaging fluid. 

In any case, the cross-section of the entrance to the orifice 
should be of such size as to reduce the entrance velocity to a 
negligible value. If the orifice needs to be large to secure the 
desired pressure drop, and the conduit is relativel}^ small, the 
purpose can be accomplished by making an enlarged section 
in the conduit. 

In the case of the Pitot meter. Test 25 (a), velocity is measured 
by measuring a static pressure caused by it. In the case of an 
orifice, the procedure is reversed in that a static pressure, caus- 
ing velocity, is measured and from it the velocity is determined. 
It follows that the derivation of the velocity formula is the same, 
and we have for an orifice after introducing the coefficient of 
discharge, 

y = c66.7V/i, for room conditions of air, 
V = cllA\l -T, for general conditions, 



27 FLOW METERS 123 

and for the rate in pounds per second, d, being the diameter 
of the orifice in inches 

the other notation being as given for the Pitot meter. 

The value of c has been fairly well established for orifices 
in thin plates, up to about 5 ins. in diameter, and to a pressure 
of about 6 ins. of water. An average value of 0.6 may be taken 
within these limits wnth less than 2 per cent of error. 

(a) Determination of Quantity Rates at Various Heads. The 
rate may be varied by varying the output or the speed of the 
machine handling the gas. If an air compressor or blower^ the 
speed may be varied. If the orifice is used for such a purpose 
as measuring the exhaust from a gas engine, its external load 
may be varied, thus changing the amount of fuel and air used. 

The true rate may be measured by any of the methods of 
Tests 25, 28, 29, or by a gasometer if the volume of gas is not too 
large. 

Readings of the pressure difference between the two sides of 
the orifice should be plotted in the gage units against true 
rates. 

(b) Determination of the Coefficient of Discharge. This 
is readily calculated from the flow formula, the calibration data 
of (a) being known. It is instructive to plot values of c against 
the pressure drop through each size of orifice, and against orifice 
diameters for each value of the pressure drop. 

Problem 27i. Write the equation of energy of air on the two sides of an 
orifice, neglecting kinetic energy at the entrance. Allowing a drop of pressure 
equal to 6 ins. of water, compare the velocity due to pressure energy with 
that due to intrinsic energy assuming adiabatic flow. 

Problem 272. Design an orifice and containing conduit to measure the 
air suppHed to a 12 H. P. gas engine taking about 20 cu. ft. of fuel gas per 
horse-power hour and about 12 cu. ft. of air to one of fuel. Drop of pressure 
through the orifice should not exceed 6 ins. of water. 



124 FLOW METERS 28 

28. Calibration of an Anemometer 

Principles. An anemometer is a meter of the velocity type, 
generally consisting of a wheel with vanes against which the cur- 
rent of gas impacts causing a rotary motion proportional to the 
velocity of the current. This motion is transmitted to a gear and 
counter combination which registers linear feet continuously. 
By counting the time, the velocity in feet per second or minute 
is calculable. 

When used to measure quantity, the anemometer is generally 
placed at the exit cross-section of the conduit discharging the 
gas. If the cross-section is rectangular it may be divided into 
a number of small squares defined, for convenience, by light 
strings or wire fastened from wall to wall of the conduit. The 
anemometer is placed in the middle of each of these squares and 
the velocity read. The average velocity through all of them 
may then be used with which to multiply the total area to get 
cubic feet per minute or second. If the conduit is round, the 
anemometer should be placed at points located as for a Pitot 
tube, Test 24 (a). 

Anemometers generally are not adapted for velocities higher 
than 100 ft. per second, and are not very reliable. The vanes 
are apt to becomxO deformed, causing false indications, and 
changes of frictional resistance of the bearings will have the same 
result. 

When the velocities exceed the capacity of the anemometer, 
the discharge conduit may be enlarged in cross-section at the 
exit. 

(a) Calibration against the Velocity of the Instrument in 
Still Air. The anemometer is mounted on one end of a horizontal 
arm 3 or 4 ft. long and pivoted at the other end so that the 
instrument may be caused to travel through the circumference 
of a circle. For this purpose the pivot may be supplied with a 
grooved wheel whereby the arm may ]je driven, through a belt, 



28 FLOW METERS 125 

by a motor or by hand. Knowing the revolutions per minute 
of the arm and its radius to the center of the anemometer, the 
linear velocity of the anemometer may be calculated. This 
is the true velocity of the air relative to the anemometer, and 
corresponds to the instrument reading. A number of such 
determinations are made at different velocities, and plotted as 
a calibration curve. 

Care should be taken that the velocity is uniform through- 
out each trial, and that the error of starting and stopping is 
made sufficiently small. A small lever is generally arranged on 
anemometers by which the recording mechanism may be thrown 
in or out of gear. This may in some cases be operated while 
the instrument is moving. 

(b) Curve of Correction Factors. Corrections may be figured 
as quantities in linear feet per minute to be added to or sub- 
tracted from the instrument indication for one minute. These 
should be plotted against linear velocities as shown by the 
instrument. 

Problem 28i. A blower discharges 2000 cu. ft. of air per minute through 
an 8-in. pipe. Design an exit conduit to reduce the velocity a proper amount 
so that the air may be measured with an anemometer, and show where the 
anemometer should be placed. 

Problem 282. If the encircling frame of an anemometer is the same 
diameter as the opening through which gas is discharged, what should be 
the area with which to calculate quantity? Examine an anemometer to answer 
this question. 

29. Testing a Calorimetric Apparatus for Measuring Gas 

Principles. If gas flowing through a conduit is arranged to be 
heated or cooled by steam, water, or electric current, then, 
barring radiation from the conduit, the heat gained by the one 
medium equals that lost by the other. Thus, supposing the r^as 
to be cooled by water pipes, if 

W = weight of gas passing in a given time, 
TF» = weight of water passing in same time, 



126 FLOW METERS 29 

Ti, 72 = initial and final temperatures of the gas, 
h, ^2 = initial and final temperatures of the water, 
Cp = specific heat of the gas at constant pressure, 

then 



from which, 



CATi~T2) 



It is thus seen that with such an apparatus the air passing in a 
given time may be measured by weighing the water and taking 
the temperatures of the gas and water before and after cooling. 

If steam is used in the coils, being condensed by the air, 
it is necessary to take the temperature of the water discharged 
and the pressure and quality of the entering steam from which 
its heat content may be obtained with the steam tables. 

If electric current is used, the heat equivalent may be figured 
from voltmeter and ammeter readings. 

The calorimetric method is sometimes useful for measuring 
large quantities of air or gas. 

The Thomas Electric Gas Meter is an elaborate apparatus 
of this type, and is perhaps the most accurate device for measuring 
gas, especially in large quantities, on the market. Resistance 
thermometers are used, by which a constant temperature differ- 
ence is maintained; and the current necessary to maintain this 
difference of temperature is measured in terms of standard cubic 
feet of air. The meter is entirely automatic and autographic. 

An advantage of this type of meter is that no corrections for 
pressure and temperature are necessary, since the indications 
are proportional to weight and, therefore, to standard cubic feet. 

(a) Examination of Instnmients. The instruments should be 
sufficiently precise that the error of reading should be less than 
2 per cent of the corresponding factor in the formula. The 



29 FLOW METERS 127 

weight of water may be measured readily with proper precision. 
The temperatures, however, appear as differences which may be 
only a few degrees. Hence, thermometers graduated to tenths 
may be necessary. It is sometimes useful to figure beforehand 
rough values of w^eights and temperature differences in order 
to ascertain the required precision of the instruments. 

It is best, when using the apparatus, to take temperatures 
at various points in the cross-section of the gas conduit, to search 
for variations. 

(b) Determination of Radiation Correction may be made 
approximately by stopping the flow of gas and maintaining the 
temperature within the conduit at an average value betw^een 
the limits in actual operation. The heat necessary to maintain 
this temperature may then be figured for a unit of time. This 
may be used as a correction if very precise results are desired. 

Problem 29i. What should be the least count of an ammeter to measure 
600 cu. ft. of air per minute under room conditions within 3 per cent of 
eiror? The voltage of the hne is about 110. What should be the least count 
of the thermometers? Temp, rise of air to be about 20° F. 

Ans.y about 2 amp. 



30. Calibration of a Steam Meter 

Principles and Types. Steam meters are built on the Pitot, 
Venturi, and orifice principles. The quantity of steam flowing, in 
pounds per unit of time, is therefore proportional to the square 
root of a pressure or difference in pressure. The differential 
pressure, varying with the flow, actuates an indicating or recording 
device. When arranged to give a time chart showing rates and 
total quantities, the recording mechanism is generally rather 
delicate and complicated. It should be noted that with such 
meters, the steam flow is proportional not to the motion of the 
indicator or height of the chart, but to the square root of these 
quantities, unless some rectifying device is employed. 



128 FLOW METERS 80 

Changes in density of the steam, due to difference in pressure 
or superheat, should be allowed for, since the meters generally 
indicate the quantity in terms of pounds. This may be done 
by applying diferent taUes, furnished by the makers, to interpret 
the indications, or by a hand adjustment of the recording 
mechanism. Variation of density due to wetness may be avoided 
by passing the stream through a separator just before it reaches 
the meter. 

The General Electric Co. steam flow meter operates on the 
Pitot principle, the static and dynamic openings being made 
through a '^ nozzle plug '' which is screwed into the steam main, 
different lengths being furnished for different diameters. The 
differential head is transferred through |-in. pipe filled with con- 
densed steam, to a cast-iron, closed mercury manometer of the 
cup type, the rising column of which supports a float. On this 
float is a vertical spindle terminating in a rack. As the float 
rises and falls with the variation of pressure made by the steam 
flow, it revolves a magnet by means of the rack and a pinion. 
Another magnet, outside the mercury container (which, of course 
is under full steam pressure), follows the motion of the inside 
magnet; and this outside magnet motion actuates the indicator 
and recording pen mechanism. The graduations of the instru- 
ment are in arbitrary units from 1 to 10. To interpret the indica- 
tions, it is necessary to.multiply by KiXKoXKsXKi determined, 
respectively, by the internal pipe diameter, quality and pres- 
sure of the steam, and the (exchangeable) size of the internal 
mechanism of the meter. Values of these quantities are fur- 
nished by the makers in the form of curves. Integration of the 
chart for total quantities may be accomplished Vvith a special 
cam-operated planimeter which corrects for the variable ordinates. 

The Curnon steam flow meter is a Pitot instrument, in which 
the differential pressure operates on a diaphragm set in a recorder 
case. The resulting motion of this diaphragm is communicated 
through an ingenious hnk-work to a pen-arm, rectifying the square 



30 FLOW METERS 129 

root motion so that the rise of the recorder pen is very nearly 
proportional to the steam flow. A feature of this instrument is 
that differences of density, accompanying variable steam pres- 
sure, are automatically corrected by a Bourdon tube. 

A Venturi steam meter is made by the Builder's Iron Foundry 
and is, in principle, identical with the water meter illustrated on 
page 110. The General Electric Co. also apply the Venturi, 
instead of the Pitot principle, with the recorder previously de- 
scribed, for pipe sizes of 2 ins. and less. 

The St. John steam meter uses the orifice principle at a 
constant difference of pressure and varies in orifice size to allow 
various amounts of steam to pass. This is accomplished by a 
float set in the orifice and so shaped that its motion varies 
the effective area of the orifice. The motion is transmitted 
to an indicating or recording device. In this case, the height 
of the diagram obtained is directly proportional to the steam flow. 

A Simple Orifice Meter. When steam passes through an 
orifice, dropping in absolute pressure from P to p, the flow 
increases with the drop until p = 0.58P, which is known as the 
'^ critical pressure. '' For lower pressures than this, there is no 
increase in the flow. 

A convenient method of orifice measurement, when the steam 
is discharged at a pressure low^er than 0.58P, depends upon 
the application of Napier's formula, namely, 

PA 



TF = 



70 



in which W is the w^eight in pounds per second of dry 
saturated steam at an absolute pressure P lbs. per square 
inch, behind the orifice, and A is the area of the orifice in square 
inches. 

Steam meters generally are not to be depended upon when 
the flow is verv variable or intermittent. This condition mav 
often be remedied by the location of the meter. 



130 FLOW METERS 30 

Integration of drum charts with uniform ordinates may be 
accomphshed with the usual polar planimeter; but for circular 
charts the methods of Test 16 (6) may be applied. 

(a) Calibration may be made by comparison with an accurate 
steam meter, or bj^ direct weighing of the steam. The latter 
method is the more dependable. All of the steam passed through 
the meter in a given time should be condensed in a surface con- 
denser and then weighed. A calibration curve may be made for 
each pressure or condition of superheat, if desired; the quan- 
tity of steam being varied by a valve in the steam line, between 
the meter and condenser. Generally it is sufficient to make the 
calibration at one condition of pressure, the steam being sat- 
urated. Throttling calorimeter readings should be made to 
insure the latter condition. The rate of flow should be kept as 
constant as possible during each of a number of runs at different 
rates, and the total condensate compared with the total obtained 
by integration of the chart, or average indications multiplied by 
time. 

Before testing, the meter should be set correct at zero 
according to the maker's directions. 

(b) Sensitiveness of recording meters may be examined by 
quickly stopping the flow of steam, and noting the time and 
character of the curve drawn when the pen returns to zero. Another 
useful test is to note the minimum amount of change in the valve 
opening regulating the flow, to produce a change in the recorder 
pen position. From this can be found the smallest change in 
the flow rate to which the meter will respond. 

Problem 30i. Using Napier's formula, what is the flow of steam in pounds 
per second through a ^-in. diameter orifice, if the gage pressure is 30 lbs.? 
What is the lowest pressure to which this method appUes if the steam dis- 
charges into the atmosphere? Ans.j 0.0314 lb. per sec; 25 lb. gage. 

Problem 3O2. Using a chart record from an actual steam meter, figure 
the average rate by taking off velocities at a number of equal time intervals. 
Figure the average rate from the mean height obtained by a planimeter. 
Compare results. 



31 THERMOMETERS 131 



THERMOMETRY 

Temperature may be defined as a measure of heat. It is 
purely relative and is generally dated from the freezing-point of 
water. 

The expansion of materials, when heated, is approximately 
proportional to the heat added. It follows that the increase of 
length of a material is a measure of heat intensity. Upon this 
principle, the mercury thermometer was devised, mercury being 
chosen on account of its expansive properties. The Fahrenheit 
scale of degrees w^as chosen in a roundabout way by its inventor, 
who exposed his thermometer first to freezing water and then to 
water at the boiling-point. He marked the stem of the instru- 
ment at the level of the mercury in each case, and divided the 
distance between the marks into 180 equal parts. He continued 
the scale below the freezing-point by 32 of these divisions. The 
freezing-point thus became 32 degrees, and the boiling-point 
212 degrees. Therefore the Fahrenheit degree may be defined 
roughly as the increase of temperature corresponding to 1-180 
of the total linear expansion of the material chosen for a ther- 
mometer between the freezing- and boiling-points of w^ater. 

The material may be liquid, solid, or gaseous. Now, no 
know^n material expands uniforml}^ in proportion to the heat 
added. The departure from uniformity, although slight, is 
appreciable in accurate work, especially at high temperatures. 
It follows that the divisions of a mercury thermometer, although 
absolutely equal, do not measure equal amounts of heat, and a 
degree of temperature is a quantity varying w^ith its location 
on the scale. Also different materials expand according to 
different laws. Consequently, two thermometers of different 
materials, standing the same at the freezing- and boiling-points 
of water, will differ at all other points. It must not be thought 



132 THERMOMETERS 31 

that this is because either one is inaccurate; it is simply that 
they are different standards. The linear expansion of a particular 
material, such as mercury, yields an entirely definite, though 
arbitrary, temperature scale, because the expansive properties 
of such a material, when pure, are constant. 

In a mercurial thermometer, however, the degree is not measured 
by the expansion of mercury only; the glass containing it also 
expands. The scale, therefore, depends upon the relative expan- 
sion of mercury and glass. The latter varies considerably both 
in manufacture and expansive properties, so that for a standard 
scale it must be specified with great care. 

Owing to the difficulty of obtaining glass of uniform quality, 
other materials than mercury have been preferred for accurate 
work. For the expansive material, air has been commonly used 
on account of its great expansiveness compared with that of the 
containing material. Nitrogen and hydrogen are now in more 
extensive use. 

Gas thermometers are of two types: constant pressure and 
constant volume. The former uses the expansive properties 
of the fluid as in the mercury thermometer, while the latter 
measures the temperature indirectly by the pressure, which 
varies directly with the temperature according to Boyle's law. 
The resulting scales are different, but the differences are so 
slight that for most engineering purposes it is not necessary to 
discriminate between them. The gas scales are very nearly 
coincident with each other and with the theoretical ^* work 
scale '' devised by Lord Kelvin. This latter is the ideal scale 
in which the degrees stand for equal amounts of heat. The 
simple mercury scale is lower than the others between the freez- 
ing- and boiling-points of water and higher above the boiling- 
point. The m.ercury-in-glass scale is higher than the others 
between the freezing- and boiling-points. 

The nitrogen scale is the one commonly employed in scientific 
work, but the standard (between the freezing- and boiling-points) 



t 



31 THERMOMETERS 133 

is that of the constant-volume hydrogen thermometer. This 
was defined in 1887 by the International Bureau of Weights and 
Measures. The standard instrument is operated at an external 
pressure of one standard atmosphere, or 760 mm. of mercury, 
and the hydrogen is maintained at a pressure, when at the 
freezing-point, of one meter of mercury. 

31. Calibration of High-reading Thermometers and 

Pyrometers 

Principles and Types. Instruments for measuring temper- 
atures above 600° F., are often referred to as pyrometers, but as 
there is no clear distinction between various devices denoted by 
this term and by the term '' thermometer,'' the latter will be 
used in a generic sense. The writer prefers to use ^^ pyrometer '' 
for thermometers applicable to flame temperatures. 

Mercury-in-glass thermometers are made for temperatures up 
to 1000° F. Their use, however, is limited because of their 
fragility and by the fact that the sensitive bulb and graduated 
scale are necessarily very close together. 

Recording thermometers with disc charts have found much 
favor in power-plant work because of their convenience and 
accuracy. These are of the constant-volume type, working, "in 
reality, as a pressure gage. The helical tube of the gage is con- 
nected by means of a flexible tube of small internal diameter to a 
bulb, and the system filled with a thermometric medium. Upon 
heating the bulb, the pressure of the medium is raised, transmitted 
to the helical tube, and recorded in terms of temperature. The 
working medium usually is a liquid for low temperatures, a vapor 
for medium, and a perfect gas for high. The first and the third 
employ charts with uniform scales, but the graduations of vapor 
(as alcohol) thermometers increase with the range. These are 
unaffected by changes of temperature of the flexible and Bour- 
don tubes. Such changes cause error with the thermometers 



134 THERMOMETERS 31 

using liquids and gases, unless equipped with special com- 
pensators. 

Another form of expansion thermometer takes advantage 
of the relative expansion of two metals. As they are heated, 
the motion of one relative to the other is magnified by a gear 
combination and transmitted so as to rotate a needle over a grad- 
uated dial, thus indicating the temperature. 

The thermo-electric couple is one of the most accurate and 
convenient instruments for measuring temperature. It depends 
upon the fact that two wires of different metals having appro- 
priate thermo-electrical properties will generate an electromotive 
force when connected at their ends, which electromotive force 
is proportional to the temperature difference between the 
ends. If it is arranged that the current be measured with a 
sensitive galvanometer, placed at any convenient distance from 
the thermo-electric ^^ couple/' w^e have an indirect measure of 
temperature. The galvanometer may be graduated in degrees or 
a calibration curve may be used to translate the electrical units. 

In the case of thermo-couples, readings should be made of 
the temperature of the ^^ cold j unction, '^ that is, the ends of the 
couple to which the galvanometer leads are joined. This is 
because the temperature indicated by the galvanometer is the 
difference between those of the cold and hot junctions. The 
cold junctions are often placed in ice to keep them at a constant 
known temperature. If a couple has been caliL rated in this 
way against a standard couple, allowance should be made for the 
temperature of the cold junction when in ordinary use. This 
may be done by adding to the indications the difference between 
freezing temperature and the temperature of the cold junction. 

For temperatures up to 1200 or 1400° F., the couple is com- 
posed of a wire of nickel and another of nickel and chromium. 
For temperatures up to 3000°, the metals are platinum and 
platinum v.'ith 10 per cent rhodium. The latter combination 
may be used for the low^ temperatures, but the former is preferred 



31 THERMOMETERS 135 

on account of cheapness. Many other combinations have been 
used, but those cited above are the most usual. 

The electrical resistance thermometer is one of the most 
accurate of temperature-measuring devices. This consists of a 
length of wire material, capable of resisting the heat, as platinum 
or nickel, the resistance of which can be measured with a Wheat- 
stone bridge. When the temperature of the wire increases, its 
resistance goes up, so that the one can be measured by the other, 
when the coefficient of resistance is known (that is, the change of 
resistance per degree of temperature). This coefficient may be 
determined with great accuracy, and from it can be plotted a 
calibration curve of temperatures against resistance. 

Optical pyrometers are advantageous when the hot body to 
be measured is inaccessible to a couple or bulb. One of them, 
the Morse, depends upon a comparison of the brightness of 
the hot body with that of an electric filament which is caused to 
glow more or less brightl}^ by varying the current passing through 
it. Then, by measuring the current, an indirect m^easure of the 
temperature is obtained as wdth the thermo-electric couple. 
When used to measure furnace temperatures in boiler testing, 
a thin plate of iron is hung at the required point and its bright- 
ness is compared with that of the filament. This type of 
pyrometer is not very precise because it is difficult to judge 
exact similarity of brightness. 

Another optical pyrometer depends upon the thermo-electric 
couple principle, but the couple is acted upon by radiant heat 
concentrated upon it by means of lenses in the form of a tele- 
scope. 

There are other forms of pyrometers using other principles, 
but the ones listed above are the principal ones. 

There are three ways generally used to calibrate high-reading 
thermometers and pyrometers : first, by comparison with a stand- 
ard or secondary standard instrument; second, by comparison 
with the temperature of saturated or wet steam determined from 



136 THERMOMETERS 31 

its pressure; third, by comparison with temperatures as shown by 
the melting-points of metals or boiling-poin-ts of fluids and salts. 

(a) Calibration against a Standard. For this purpose, mer- 
cury thermometers may be used for temperatures up to 1000° F. 
Above, and often below^ that temperature, a favorite instrument 
is the thermo-electric couple, as it is one of the most accurate 
and easy to use. 

The temperature is varied in a gas or electric furnace in 
which the bulbs of the standard instrument and the one to be 
tested are placed. Care should be taken to bring the whole 
furnace up to a uniform temperature before recording observations, 
by allowing sufficient time for heating. The sensitive portions 
of the two instruments should be placed as close to each other 
as possible to avoid errors from locahzed temperatures. It is 
best to take a series of decreasing readings to supplement the 
increasing ones, allowing the furnace to cool for this purpose. 
If the up and down readings are different at a given temperature, 
as they will be w^ith certain types of instruments, they should be 
averaged. (See Test 2, principles.) 

(b) Calibration against Steam Temperatures. This method 
is limited by the available pressure. At 200 lbs. gage, the tem- 
perature is 388° F., and at 500 lbs., about 470 degrees. It is 
thus apparent that not very high temperatures can be reached 
with saturated steam. 

The procedure is to vary the temperature in a steam cham- 
ber similar to that used for testing indicator springs, Fig. 33, 
page £4, by controlling the pressure. The thermometer is 
inserted in a well set in the chamber and readings taken of it 
and of an accurate and sufficiently precise pressure gage at each 
variation of the pressure. The actual temperatures are ascer- 
tained by reference to the steam tables. A barometer reading 
is necessary to get absolute pressures. 

^^hcn the steam is throttled to reduce its pressure it may 
Leconie superheated, in which case its temperature is not deter- 



31 THERMOMETERS 137 

minable. To avoid this, water may he sprayed into the steam 
before it enters the steam chamber, or the chamber may be water- 
jacketed. It is essential that there should be definite knowledge 
of the steam's wetness, for which purpose a throttling calorim- 
eter (see Test £2) may be referred to. 

A calibration of an instrument indicating beyond the available 
temperatures may be had by exterpolation. That is, after the 
experimental data have been plotted, the curve is continued 
beyond the known points. If the curve is a straight line, the 
result may be good, but caution should be used not to extend 
the exterpolation too far. 

(c) Calibration against Melting- and Boiling-points. This 
method will be found quite convenient for ranges between 200° 
and 800° F. Its accuracy depends upon the purity of the materials. 

When using the liquids and salts, they may be boiled in Florence 
flasks over a Bunsen burner, and the thermometer should 
preferably touch the liquid as well as be surrounded by the 
vapor. The following materials may be used : 

Water, boihng at 212° F. 

Aniline, boiling at 365° F. 

Naphthaline, boiling at 420° F. 

Diphenylamine, boiling at 590° F. 

Anthracine, boiling at 664° F. 

Zinc, melting at 786° F. 

Sulphur, boiling at 832° F. 

Antimony, melting at 1167° F. 

(d) Stem Corrections. If a mercury thermometer is to 
indicate correctly, all of the mercury, both in the stem and bulb, 
should be subjected to the measured temperature. In practice 
this is rarely the case, as part of the stem containing mercury 
is at or near room temperature. For accurate work it is then 
necessary to apply a '^ stem correction.'' 



138 THERMOMETERS 31 

Let *S = stem correction in degrees; 

fl' = height of column above actual position of mercury, 
if uniformly heated, inches; 
Z = length of one degree on the stem, inches; 
A^ = number of degrees on the stem exposed to room 

temperature; 
r = tem.perature, Fahrenheit, of the bulb; 
^ = average temperature, Fahrenheit, of the exposed 

mercury and stem; 
C = cubical coefficient of expansion of the glass and 
mercury, combined by subtracting the value of 
one from that of the other. 



Then 

Also 



H = C{lXX){T-t) 
H 



-'-T 



Hence 

S = CX{T-t). 

The value of C for the Fahrenheit scale may be taken as 0.000088 
and fcr the Centigrade scale, 0.00016. 

It is generally sufficiently accurate to take the actual read- 
ing as the value of T. If desired, the corrected temperature thus 
obtained may then he used as T, and a second and more nearly 
exact stem correction calculated. 

The value of t is somewhere between room temperature 
and that of the bulb. It is often estimated by hanging a second 
thermometer against the one to be corrected, vith its bulb at 
a middle point on the exposed mercury column. It is very 
doubtful that this yields a close value for t, 

^^ hether or not a stem correction is necessary depends upon 
the purpose for which the temperature is measured. In engineer- 
ing work, thermometers are generally used to measure tem- 
perature differences, so that the percentage of error in the result 



32 STEAM CALORIMETERS 139 

may be based upon a much smaller quantity than the actual 
number of degrees read. In many cases, when the temperatures 
are comparatively low or when the stem is well immersed, the 
correction is negligible. 

Problem 31i. A thermometer reads 2<^° when it is immersed to the 60° 
graduation. If temperature of room is 80°, what is the actual measured 
temperature? Estimate the stem temperature as an average of room and 
indicated temperatures. Ans., 241.4°. 

Problem 3I2. What should be the least count of a pressure gage to cali- 
brate by steam a thermometer whose least count is 2 degrees? Whv? 

Ans., 1 lb. at 300°. 

Problem 3I3. Account for the differences between up and down readings 
in the calibration of a thermo-electric couple. 



HEAT OF STEAM— CALORIMETRY— SAMPLING 

The English measure of heat is the British thermal unit, or 
B.t.u. This is loosely defined as the amount of heat necessary 
to raise the temperature of 1 lb. of water 1° F. As the specific 
heat of water varies with the temperature, a precise definition 
should name the temperature range. Several ranges have 
been used, as 32 to 33 degrees, 39 to 40 degrees, 61 to 62 degrees, 
so that there are a number of values for the. B.t.u. The 
present tendency favors the '' mean B.t.u.'' which is the 
average amount of heat per degree required to raise a 
standard pound of water from the freezing- to the boiling- 
point. One advantage of this unit is that it is independent 
of the temperature standard (whether gas or mercury) since 
it is fixed by the two temperatures which are the same on all 
thermometric scales. This is the unit used in the Marks and 
Davis' steam tables, values from which will be used in the 
examples in this work. 

The heat of steam is counted from a temperature of 32° F. 
and is the amount of heat necessarV to convert 1 lb. of water 



140 STEAM CALORIMETERS 32 

at that temperature into steam under the given physical condi- 
tions. This includes the heat added to the liquid to bring it 
to the boiling-point at the given pressure, and the heat then 
necessary to vaporize it. If the steam is superheated, still 
another amount of heat is added to it to raise its temperature 
from that at the boiling-point, the pressure remaining the same. 
All of these heat quantities depend upon the pressure of the 
steam. It is thus seen that the physical conditions of steam 
determining its heat content are, first, its pressure, and second, 
its wetness or superheat. For example, the heat of the liquid, 
referred to as h, of steam at 14.7 lbs. absolute, is 180 B.t.u., 
being the heat necessary to raise the temperature of 1 lb. of water 
from 32 to 212°; 970.4 B.t.u. are then necessary to vaporize 
it. The heat of vaporization is referred to as L. Thus the total 
heat, //, necessary to make 1 lb. of dry steam at 14.7 lbs. is 
h+L = l\50A B.t.u. If less than the w^hole poimd of water 
has been evaporated so that there is 1—x lb. of water as a 
mixture, x being the part of a pound actually evaporated, then 



H = h+xL. 






This is the generic expression for the heat added to make 1 lb. 
of wet steam in which x may have any value up to unity. 
For superheated steam the generic expression is 

H = h+L+Cj,{T-ts), 

in which Cp is the specific heat of superheated steam, ts is the 
temperature of the dry or ^^ saturated '^ steam at the given 
pressure, and T is the temperature of superheat. The value 
of Cp varies with T and with the pressure. 

These various physical conditions are represented by Fig. 68, 
which shows 1 lb. of H2O in a cylinder with a movable end under 
a pressure P. 



32 



STEAM CALORIMETERS 



141 



It should be remembered that the datum temperature of 32'' 
is taken purely as a matter of convenience, and that the actual 
amount of heat contained by steam, or for that matter any 
material, is a relative quantity. The significance of heat quan- 
tities so counted enters when we take the difference between 
two of them representing two conditions of H2O. Thus the heat 
per pound given up by a boiler in making steam is the difference 
between the heat content of the H2O leaving the boiler, counting 
from 32°, and that of the feed-water entering, counted 
ein ilarly. 



Af 

Freezina 

Point 



m 



Boilinc^ 
Point- 



^r:-52im 



-t°= 



Parfly 
Vaporized 



I r I rijiiii 



%Lb.5feoirri- 

'1:XLby(afer 



lllllj!! iflllllli 



Saturated 
■•'Steam':' 



t^. 




Heat added- 



■h 



"h-xL 



^H*L =h*XL*CpCr-iO 



Fig. 68.— Heat Added to One Pound of H2O. 



To measure the heat of a given quantity of steam, it is neces- 
sary to know the amount in pounds and the heat content, i7, or 
heat added per pound; the one multiplied by the other gives 
the heat of the total quantity. The weight of steam may be 
obtained by a steam meter, Test 30, or by any of the methods 
given under engine or boiler testing. The steam tables are used 
to get the value of Hy since they list the heats of liquid and 
vaporization at different pressures. If the steam is dry, it is 
sufficient to take its pressure or temperature for reference in the 
tables. If it is superheated, its pressure should be read, and 
its temperature, T, The steam tables furnish values of is, and Cp, 
from which H may be calculated, knowing also h and L, The 
steam tables also contain heat contents of superheated steam, 
so that the calculation is not always necessary. 



142 STEAM CALORIMETERS 32 

If the steam is ^vet, the value of x, as well as the pressure 
or temperature, must be known to fix its heat content. This 
is the condition generally met in practice, which makes deter- 
minations of wetness or '' quality " important, especially for 
engine and boiler tests. 

The Heat of Steam when Mixed with Perfect Gases. If the 
pressure of the steam were known, its total heat could be found 
by reference to the steam tables as previously described. When 
steam is mixed with other gases, however, its pressure is less than 
that of the mixture. This follows from Dalton's law, which may 
be stated thus: 

In a gos mixture occvpying a given volume^ the pressure of 
each constituent gas is the same as though it occupied the volume 
alone, and the pressure of the mixture equals the sum of the pressures 
cf the constituent gases. 

For example, 

1 cu. ft. of air at 60° F., and 14.7 lbs. pressure weighs 0.0764 lb. 
1 cu. ft. of steam at 60° F., and 0.256 lb. pr. weighs 0.00083 lb. 
1 cu. ft. of mixture has a pressure of 14.956 lbs., weighs 0.07723 lb. 

The figures here given for the steam apply to the saturated 
condition. At the temperature named, no greater weight of 
steam than 0.00083 lb. could exist in one cubic foot of volume, 
whether that volume were also occupied with another gas or 
not, because if there were more than this amount of H2O present, 
its density would be greater than that of saturated steam 
at 60°, and consequently some of the H2O would be in the 
form of water. On the other hand, at this temperature, there 
may be less than the nam.ed amount of steam present. In 
such a case, the pressure of the steam is less tl an 0.256 lb., 
since there is less of it, and therefore it is at a temperature 
higher than that due to saturation; that is, the steam is then 
superheated. This is the form in which humidity in the atmos- 



32 STEAM CALORIMETERS 143 

phere usually exists. It is also the form in which H2O appears 
in the products of coml:ustion of fuels. 

Consider now how the total heat of superheated steam in 
such a mixture may be determined. Let P and T stand for the 
absolute pressure in pounds per square foot and the absolute tem- 
perature in degrees Fahrenheit respectively, of the mixture. 
These quantities are readily measurable. Also it is possible 
to figure the weight of one cubic foot of the gases exclusive of 
the steam, and the weight of steam in one cubic foot of the 
mixture. Now the pressure of the gases exclusive of steam 
may be figured from the relation PiVi = RT, in which Pi is the 
desired pressure, Fi is the reciprocal of the weight of the gases 
per cubic foot, and R may be obtained from works on thermo- 
dynamics. (For air, 72 = 53.4.) Then the pressure of the steam 
equals 

Knowing the pressure of the steam, values of /i, L, and saturation 
temperature, tsy may be found from the steam tables; which 
values, together with the temperature of superheat, T, make 
possible the calculation for total heat, H^ according to the expres- 
sion previously given. (See also ^' Hygrometry,'' Appendix.) 

This calculation is laborious, so the following m^ethod, suf- 
ficiently accurate for engineering purposes, is preferable. The 
total heat of steam in the form of humidity in air or gases of 
combustion equals 1058.7+0.455 Te, in which Te is the tem- 
perature in degrees, Fahrenheit, of the mixture. This is an 
empirical relation proposed by Professor Diederichs. 

In the analyses of boiler, gas engine, and gas producer 
trials, the heat of the steam in the exhaust gases, counting from 
room temperature, is required. The heat in the H2O before 
vaporization is ^ — 32, t being the room temperature. Sub- 
tracting this from the expression just given, we have, roughly, 

1090+0.46 Te-t. 



144 STEAM CALORIMETERS 32 

Steam calorimeters are instruments for measuring the 
quality of wet steam. Various forms are made depending 
upon different principles. These depend either upon a trans- 
fer of heat by which it can be equated to a measurable quan- 
tity or upon the mechanical separation of the entrained mois- 
ture. The first is strictly a calorim.etric process. Thus if a 
sample of the steam whose wetness is to be measured is con- 
densed in water, the heat given up to the water is readily meas- 
ured, and this quantity can be equated to h+xLj in which x 
is unknown. The equation then yields the value of x. Another 
method is to superheat the steam, in which form its heat con- 
tent is readily measured. 

The mechanical separation m.ethod uses an apparatus similar 
to the ordinary steam separator, and involves weighing both 
the steam and the separated water. 

Sampling. As usually arranged only a small sample of the 
total steam is tested for a quality determination. The accuracy 
of the result is primarily dependent upon the representativeness 
of the sample, so that every care should he used to secure a cor- 
rect one. Unfortunately, it is always uncertain that a reason- 
aV)ly accurate sample has been obtained, but by using the 
proper shape of sampling pipe, inaccuracy may ]}e reduced to a 
minimum. 

In a horizontal steam pipe, water is r.,pt to run along at the 
bottom, separated from the steam. If ai) cf this water is passed 
into the sampling pipe, an undue amount 
of water appears in the sample. In a \--. --/n6.DiaofMarr>->^ 
vertical pipe moisture runs down the BBll^^^^^^^^ 1 
inside of the pipe wall. Undoubtedly \p,]:Jj^^' ^\SJi 



, . ify'^'ir'^ , ■■-Slots fof^cc 

some of this should be included m the P-pe Thread. stream. 

sample, but it is no easy matter, theo- Fig. 69.— Sampling Pipe. 

retically or practically, to secure the 

right proportions. Fig. 09 sho^^ s an approved form of sampling 

tube. 



32 



STEAM CALORIMETERS 



145 



32. The Throttling Calorimeter 

Principles. Fig. 70 represents the instrument diagrammatic- 
ally. Steam from a sampling tube enters the steam pipe from 
which it passes through the orifice 0, about yq in. in diameter, into 
the chamber C, which is open to the atmosphere. The steam is 

throttled upon passing through the ori- 
fice, and drops to a pressure only a little 
in excess of atmospheric. Now the heat 
contained b}^ 1 lb. of steam at high 
pressure is greater than the heat con- 
tained at low pressure, if superheat does 
not exist. Upon reaching the chamber, 
C, the steam therefore contains an excess 
of heat, and this excess goes to evapo- 
rate the moisture carried in wath the 
steam and to superheat both. In this 
condition, the heat content is readily 
measured, which makes possible a heat 
equation involving one unknown. Before 
entering the orifice, the heat of 1 lb. of 
the H2O is hi +xLi. (See page 140 for notation.) In the calorim- 
eter chamber, it is /?2+L2+Cp(r2 — fe). Neglecting radiation, 




ii! I 



Fig. 70. 
Throttling Calorimeter. 



from which, 



hi+xLi = h2+L2+Cp{T2-t2) 
h2+L2+Cp(T2-t2)-hi 



X 



The values of h and L and (2 are found from the steam tables, 
by reference to the pressures indicated by the pressure gage P 
and the manometer M, Fig. 70. A barometer should be read 
to reduce these pressures to absolute. The temperature T2 
is obtained from the thermometer K. At atmospheric pressure 
Cp equals 0.47, but for rough and ready calculations it may be 
taken as 0.50. 



146 STEAM CALORIMETERS 32 

Certain approximations in the use of the above formula may 
be made to simplify calculations, which, in view of the uncer- 
tainty of sampling, give an ample degree of accuracy. Thus, 
the pressure in the calorimeter chamber generally is only a few 
inches of mercury, above atmosphere. If it is taken as 14.7 
lbs. absolute, 7^2+^2 = 1150, and ^2 = 212. This obviates the 
use of the manometer and barometer. Then the equation 
may be w-ritten 

1150-/U , .47(^2-212) 



x = 



Li ' Li 



If the pressure on the entering side fluctuates but little, say 
5 or 10 lbs., constant values of Iti and Li may be applied. Now, 
a value of x may be calculated for 72 — 212 = 0, taking hi and 
Li at an average pressure. The increment of x corresponding 
to one degree of superheat should then be figured. It is then 
a simple matter to add to x (when T'2 — 212 = 0) the increment 
corresponding to any number of degrees of superheat. 

For example, w^hen the average pressure is 100 lbs. gage 
hi = 308 and Li = 880. With no superheat, a: = (1150-/ii)^Li = 
(1150-308)-^880 = 0.956. To this must be added for each 
degree of superheat an amount equal to 0.47 X (1°) ^880 = 0.00053. 
If the thermometer in the calorimeter chamber shows 222°, the 
superheat is 10° and the quality of the steam is 0.956 + 10 X 
0.00053 = 0.961, and so on. This method of calculation is 
convenient for use during an engine or boiler test, since the 
quality is readily figured from the thermometer reading only, 
once the constants as oljtained above are know^n. 

The errors of tlie throttling calorimeter are due mainly to 
false thermometer readings of the superheat, and to radiation 
of heat from the instrument or fittino;s. It is best to set the 
thermometer in the calorimeter without using a well, which 
m.ay be readily done with a perforated plug of wood or rubber. 
The thermometer should be moved vertically in the calorimeter 



32 



STEAM CALORIMETERS 



147 



until the hottest part is found when the steam is passing as in 
regular use. To avoid radiation, all the parts should be well 
lagged. Not too large an orifice should be used, as this raises 
the back pressure in the calorimeter, and passes more steam 
than necessary. 

(a) Determination of the Radiation Correction is sometimes 
made for extremely accurate work. For this purpose the heat 
equation should be written 



<•- Thermometer 



.-■Pressure Caofe 
Drymcj Coil 



in which R is the heat radiated from the calorimeter from each 
pound of steam. 

Using an apparatus like that shown diagrammatically by 
Fig. 71, the entering steam may be completely dried. The 

value of X is then unity, and the above 
equation may be solved for R. The 
correction R may then be applied to 
find more accurate values of the quality 
when the instrument is in ordinary use. 
Strictly speaking, the correction applies 
only to the pressure, room temperature, 
and orifice of the test. The first two 
items may vary considerably without 
much change in the correction. 

A more convenient form for the ra- 
diation correction may be had by figuring 

' 1 1 1 ^ ^^ ^^ ^ number of degrees to be added 

\iteam to the thermometer readings. 

Fig. 71. The proper amount of heat to dry the 

entering steam is maintained by regu- 
lating the current through the drying coils. This may be done 
by using a water, or other type, rheostat in the line. In order 
to be sure that the steam is dry, one or two degrees of superheat 




l-KW^ 



148 STEAM CALORIMETERS 32 

may be carried as shown by the thermometer in the drying 
chamber, its reading being compared with the temperature cor- 
responding to the pressure, as given by the steam tables. 

Problem 32i. Pressure of steam in the calorimeter chamber is 1.5 ins. 
of mercury. Barometer is 30.3 ins. of mercury. If the steam were saturated 
in the chamber, what would the temperature be? If the thermometer 
indicates 280°, how many degrees of superheat ar6 there? What is the total 
heat of the steam in the calorimeter at 280°? If the pressure of the 
incoming steam is 84 lbs. gage, what is its quality? Ans., x= .995. 

Problem 322. Figure the quaHty from the data given in Problem 32i, 
assuming the calorimeter pressure to be equal to atmospheric, 14.7 lbs. What 
is the percentage of error? 

Problem 323. Figure the quaHty of steam corresponding to superheats 
of 25, 45, and 65°, using the approximate method of constants for Problem 32 1. 

Ans.y .972, etc. 

Problem 324. What is the maximum degree of superheat that it is pos- 
sible for the steam in the calorimeter to attain if the steam pressure is 95 
lbs. gage, and the calorimeter pressure 14.7 lbs. abs.? What is the maxi- 
mum if the steam pressure is 65 lbs. gage? 

Problem 325. What is the maximum percentage of moisture that can be 
shown by a calorimeter under the two conditions named in Problem 324? 
If the calorimeter pressure is reduced to 10 lbs. abs. by connection with a 
condenser, what then is the maximum percentage of moisture? 

Problem 326. If a thermometer reads 3° low on account of radiation, 
what is the percentage of error resulting from ignoring the radiation cor- 
rection? Use the data of Problem 32i. Ans., 0.17%. 



33. The Separating Calorimeter 

Principles. If the water entrained in steam is mechanically 
separated, and the weights of the dry steam and separated water 
are then measured the percentage of water may be readily 
calculated. IVIechanical separation may be effected by deflect- 
ing the steam and water through a sharp bend; the water is then 
thrown out by centrifugal force. 

Fig. 72 shows diagrammatically the Carpenter separating 
calorimeter. The water collects in the calibrated chamber C 
and its amount is measured by the scale S placed against a 



33 



STEAM CALORIMETERS 



149 



Steam 
Sample 



gage glass. The weight of dry steam is measured by the orifice 
method according to Napier's rule (see p. 116), the orifice being 
located at 0. Since the weight of steam discharged from an 
orifice into the atmosphere equals a constant times the absolute 
pressure, an ordinary pressure gage G may be calibrated to 
indicate the weight of steam passing per minute. In opera- 
tion, a steam sample is passed through the calorimeter, and, 

after it is thoroughly heated, initial and 
final readings of the water level are made 
for a measured interval of time, together 
with a number of readings of the gage 
^113) from which an average is calculated. The 
gage gives the pounds of dry steam passing 
per minute; multiplying this by the number 
of minutes gives the total weight of steam. 
This weight is then divided by the sum 
of the weights of water and steam to get 
the quality. 

The chief advantage of the separating 

over the throttling calorimeter is that it is 

operative no matter how low the quality. 

Experiments have shown that complete separation of the water 

may be depended upon with a properly designed separator. 

(a) Calibration of the Dry Steam Meter may be made as for 
Test 30 (a). A calibration curve for the gage should be 
plotted. 

(b) Calibration of the Water Gage. The chamber C, Fig. 72, 
is allowed to fill with water separated from steam passing as in 
usual operation. A small amount of this water is then drawn 
off from the pet cock P into a flask of cold water (to prevent 
evaporation). The weights of the flask and contents and the 
heights of the levels in the water gage before and after the oper- 
ation are carefully measured. A number of such determinations 
furnish the data for a calibration curve. 




Fig. 72. — Separating 
Calorimeter. 



150 STEAM CALORIMETERS 33 

If the water used for the calibration is cold, its weight 
should be corrected for the difference in density due to the 
different temperatures. The temperature in usual operation 
may be taken as that of the steam passing through the calo- 
rimeter. (See Appendix for density of water.) 

(c) Determination of Radiation Correction. Radiation from 
the instrument may cause a greater amount of water to be thrown 
down than was in the sample. In the Carpenter instrument, 
on account of the steam jacket arrangement (see Fig. 72), 
radiation occurs after the steam has left the separator; the water 
gage then remains correct, but the orifice measurement may 
be faulty since the orifice passes wet instead of dry steam. If 
the gage has been calibrated for the particular conditions of 
radiation, this calibration takes care of the radiation correction. 

If radiation causes an increase of water in the water gage 
the correction may be determined as follows: Dry steam 
should be supplied to the calorimeter either with an apparatus 
as described under Test 32 (a) or by taking the sample from 
another steam separator. Any water that shows at the water 
gage of the calorimeter is then due to radiation. If it is figured 
as so many pounds per minute, the correction in ordinary use 
is readily applied. 

Problem 33i. If the water gage has been calibrated using the water 
separated from steam at 100 lbs. gage, what percentage of error will there be 
when the instrument is used for steam at 50 lbs. gage, the error being due 
to the change in density of the water between the two temperatures? If 
the water in the gage glass is 150° F., due to radiation, and the water in the 
calorimeter chamber is 325° F., will the level in the glass be above or below 
the inside level? Will these errors make material error in the results of x and 
why? Ans., 2.4%. 

Problem 332. If the orifice of the separating calorimeter is used as part 
of a throttling calorimeter so as to allow for moisture escaping the separator, 
deduce a formula for the quality of the steam in terms of the weights shown 
by the separating calorimeter and the quality (xi) as shown by the throttling 
calorimeter. 



34 STEAM CALORIMETERS 151 



34. The Condensing Calorimeter 

Principles. If a sample of steam the quality of which is to 
be determined, is condensed either by mixing with or radiating 
through coils to water, the arrangement constitutes a condensing 
calorimeter. 

Let TFs = weight of condensate, including moisture in 
sample; 
h, L, x = heat of the liquid, latent heat, and quality of 
the steam sample; 
Wtc = weight of condensing water; 
^M, == temperature of water before it is heated; 
Twj = temperature of water after it is heated; 
Ts = temperature of the condensate. 

If condensation is accomplished by mixing, Tw = Ts, otherwise 
they have different values. Now, if the calorimeter operates 
continuously, and if radiation is neglected 

Ws{{h+xL)-{Ts-32)} =W^,{T^-Q. 

That is, the heat lost by the steam equals that gained by the 
water. 

If the operation is not continuous, the material of the calo- 
rimeter absorbs an amount of heat v/hich must be accounted for. 
This quantity is called the ^^ water equivalent,'' being the weight 
of water that absorbs the same amount of heat for a given tem- 
perature rise as does the calorimeter. For non-continuous 
condensing calorimeters, the water equivalent should be added 
to Tf «,. 

The equation may be solved for x, the other quantities being 
obtained experimentally, h and L are found from the steam 
tables, the pressure of the steam being observed. 



152 STEAM CALORIMETERS 34 

A barrel of water on a platform scales makes a non-con- 
tinuous mixing calorim.eter. An injector may be used as a con- 
tinuous mixing calorimeter. A surface condenser may be arranged 
as a continuous non-mixing calorim.eter. 

(a) Determination of the Water Equivalent. The condenser 
should be isolated and filled with water either hotter or colder 
than the material of the calorimeter. The initial and final tem- 
peratures of the water, h and toj and the weight of water 
W should be observed. If Q is the water equivalent, and t is 
the initial temperature of the calorimeter, then 

W(tl-t2)=Q{t2'-t) 

since the heat lost by the water equals that gained b}' the calo- 
rimeter, or vice versa. This equation ma}' then be solved for Q. 

The equation neglects radiation. To avoid the consequent 
error, a second test may be m.ade with the temperatures of 
calorimeter and water so adjusted that the temperature rise 
up to room temperature approximately equals that above. 

For example, suppose that for the first test water at 110° F. 
cools to 80°, raising the temperature of the calorimeter from 
that of the room, 70°, to 80°. The rise of temperature of the 
calorimeter during the test is 10°. Now, if its initial temperature 
were 65° and its final 75°, radiation to and from the room would 
be balanced. Hence, for the second test, the calorimeter should 
be previously cooled to 65°, and then heated with water at 105° 
so that the 30° drop in the water temperature, noted in the first 
test, will bring the final temperature to the desired 75°. The 
variation will not, of course, be exactly equal above and below 
the room temperature, but by this method the effect of radiation 
upon the accuracy of the determination of the water equivalent 
is made negligil)le. 

The student should note the fact that radiation thus taken 
care of is an entirely different quantity from that which occurs 



34 STEAM CALORIMETERS 153 

in the usual operation of the instrument. For accurate work, 
the latter should be taken into account as follows. 

(b) Determination of the Radiation Correction. For non- 
continuous condensing calorimeters such as the barrel calorim- 
eter, radiation correction may be avoided in actual use in 
exactly the same way as that described for the water equivalent 
determination. The flow^ of steam into the calorimeter is con- 
tinued sufficiently long to raise the temperature of the cold 
condensing water as much above room temperature as it was 
below. 

For continuous calorimeters, the radiation correction must 
be found and applied in the equation, as follows, 

W^{{h + xL)-{Ts-^2)]=W^,{T^,-tJ+R 

= W^,{T^+t'-Q, 
in which R is the heat radiated from Wu, lbs. of cooling water and 

To find t\ the calorimeter is operated as in usual practice, 
except that dry steam is furnished to it either by the method of 
Test 32 (a) or by using a steam separator. The value of x is 
then 1, and the equation may be solved for t\ 

The correction applies only to the temperature conditions 
of the radiation test. If the conditions in ordinary operation are 
markedly different, the radiation test should be repeated to fit 
the new conditions. It is possible, however, to keep the initial 
and final temperatures of the cooling water practically the same 
for different conditions of the steam samples by varying the rate 
of cooling water. If this is done, and if the room temperature 
is not very variable, only a single value of the radiation correction 
is needed. 

Problem 34i. The data from a barrel calorimeter determination are as 
follows: Weight of water in barrel before condensing =350 lbs., temperature 
= 55® F. Weight after condensing = 370.6 lbs., temperature = 115°. Pressure 



154 FRICTION TESTERS 35 

of steam sample = 100 lbs. gage. What is the quahty, neglecting the water 
equivalent and radiation? Ans.y 0.901. 

Problem 342. A water equivalent determination for the preceding 
example shows that 300 lbs. of water will fall from 98.6° to 97.3° F. when 
placed in the barrel at 60°. What is the water equivalent, and what is the 
corrected value of the qualit}^? Ans.y 10 lbs.; 0.934. 

Problem 343. The circulating water in a surface condenser rises in tem- 
perature from 50° to 86° F., 275 lbs. being used to condense 10 lbs. of a steam 
sample at 80 lbs. gage. The temperature of the condensate is 98°. What 
is the quahty of the sample? Ans.y 0.856. 



FRICTION 

Friction is the force which resists the relative motion of 
two bodies in contact, and is due to the interference of their 
particles at the siu'face of contact. The laws controlling this 
force are different depending upon whether the rubbing materials 
are fluid or solid. Solid friction may be either from sliding or 
rolling contact, but in this work sliding friction only will be 
considered. There is a third case, generally of greatest impor- 
tance to the mechanical engineer, namely, the friction of lubri- 
cated solids. The controlling laws fall between those for solid 
and fluid friction, resembling the one or the other according to 
the amount of lubrication. 

The laws of fluid friction are well established, but this is 
unfortunately not true of solid friction. An understanding of 
the latter is important in the analyses of friction drives, belt 
forces, etc., and important also to our knowledge of lubricated 
friction since the rubbing action of solids is a limiting condition 
of lubricated machine parts. 

It has generally been assumed that the friction between two 
dry solids is a constant fraction of the normal force pressing the 
solids together, independent of the area of contact and velocity 
of sliding, and depending only upon the nature of the surfaces. 
These hypotheses have been discredited, but, thus far, experi- 



35 



FRICTION TESTERS 



155 



mentation upon this subject has not proceded enough to give 
us more than an idea wherein they are fallacious. It is possible 
that they are true for certain materials or certain conditions, 
but unquestionably they are not generally true. 

The variation of friction, in the general case, depends upon 
the normal force between the surfaces, the amount of contact 
area, the velocity of sliding, and the materials of the bodies. 

The following table is arranged to give a ready comparison 
of the several cases. It should be remembered, however, that 
the statements under solid and lubricated friction are not well 
established, and are possibly subject to exceptions. 

VARIATION OF FRICTION 





Fluid. 


Solid. 


Lubricated Solid. 


Contact area. 


Directly proportional. 


Independent 
(approx.) 


Directly proportional. 


Velocity. 


Directly proportional 


Inversely, at a 


Inversely for low 




as the square, ex- 


diminishing 


speeds, directly as 




cept at low speeds. 


ral^e. 


square root for high 
speeds. 


Character of 


Independent. 


Varies. 


Varies. 


surface. 








Normal force. 


Independent. 


Directly pro- 


Independent. 






portional. 





It is further known that the frictional resistance to a fluid mov- 
ing upon a solid is related in some way to the viscosity of the 
fluid, decreasing as the viscosity decreases. This property has 
an important bearing upon lubricated solid friction because the 
viscosity of lubricants varies with temperature, thus introducing 
another variable in this case. 

For solid friction, the working hypothesis is that 



F=^fN 



156 



FRICTION TESTERS 



35 



in which F is the force of friction, N the force normal to the 
rubbing surfaces, and / a number less than one called the " co- 
efficient of friction/' 



35. Oil Testers 



Principles. Oil testers are instruments for determining the 
coefficient of friction in the case of lubricated solids. Their 
operation generally depends upon the balancing of the friction 
by a static moment which can be measured; from this and the 
constants of the instrument, the coefficient may be calculated. 
Referring to Fig. 73, aS is a revolving shaft to which is fitted a 
bearing carrying a pendulum. It is arranged 
that the bearing swing freely and bear on 
the shaft with a measured force, iV. The 
oil to be tested is fed to the bearing, and the 
shaft caused to revolve in a clockwise direc- 
tion. The force of friction then swings the 
pendulum to such an angle as to establish 
equilibrium. If the radius of the shaft is r ft., 
then the moment of the frictional force, fN, is 
fNXr, The weight W of the pendulum acts 
on an arm of 72 sin ^ , i? being the distance of 
the center of the weight to the center of the shaft ; consequently 
the moment of the pendulum equals WXR sin A. As this 
moment equals the moment of the frictional force, we have 




RsinA") 



KiG. 73. 
Oil Tester. 



and 



fNr = WR sin A, 

WR sin A 



f= 



Nr 



For a given set of conditions, all of the quantities on the right 



35 FRICTION TESTERS 157 

of the equation are constant except sin^, which thus becomes 
a measure of /. 

The Thurston oil testing machine depends upon this prin- 
ciple. The force N is applied and varied by means of a spring 
mounted on the pendulum, by tightening which the two parts of 
the bearing may be clamped more or less tightly together. The 
total force, A', equals twice the tension of the spring plus the weight 
of the pendulum. There are a pointer and scale on the pendulum 
by which the total force may be read directly. Another pointer 
on the pendulum moves over a stationary scale graduated to 
values of WR sin A-r-r. A thermometer well is provided in the 
upper bearing so running temperatures may be ascertained. 

The Riehl6 oil testing machine carries a hand screw for apply- 
ing the pressure, and the pressure is measured by means of a 
scale beam. A second scale beam measures the moment of the 
turning force induced by friction. By equating this moment 
to fNr, as in the Thurston machine, the coefficient of friction 
may be obtained. 

(a) Constants of the Instrument. In the Riehl6 machine, 
the only constant generally necessary to test is the value of r. 
If desired the indications of the beams may be tested according 
to the principles of Test No. 1. 

With the Thurston machine, it is necessary to find WRy r, 
and to test the spring. 

To find WRy the pendulum should be swung to a horizontal 
position and supported on a pedestal resting on a platform scales. 
A test is then made similar to that for the unbalanced weight 
of a Prony brake, Test No. 6 (a). The result should be multi- 
plied by the horizontal distance between the point of application 
of the pendulum on the pedestal and the center of motion of the 
pendulum. This gives the desired moment, WR. 

In addition to measuring the radius of the bearing, r, its 
length should be determined, so that the bearing pressure in 
pounds per square inch of projected area may be calculated. 



158 



FRICTION TESTERS 



36 



The graduations on the stationary scale may be tested with 
these data V.)y calculating their values at any values of the angle A. 

To test the indications of the spring its scale should be 
determined according to Test No. 2. As the spring is a heavy 
one, a strength testing machine is required to compress it. 

Problem 35i. Run a series of tests with an oil testing machine to show 
the relation between coefficient and load in pounds per square inch. 

Problem 862. Run a series to show the relation between coefficient and 
velocity. 

Problem 383. Run a series to show the relation between coefficient 
and temperature. 



36. Belt Testers 



Transmissioji Front/ Brake 
'Dynamomefer | — -^ ..Z— <— -- ^ 



Principles. When power is transmitted from one shaft to 

another by means of a belt run- 
ning on puUeySj friction is the use- 
ful force. Friction sets up ten- 
sions in the belt; on one side, 
a greater amount T\ , and on the 
other a lesser, T2 (see Fig. 74). 
The difference between these 
tensions is the net force, T. which effects a turning effort of the 
follower. It is shown in works on machine design that 




tll'lTy'^'^olloyrer^ 



Fig. 74.— Belt Tester. 



^ = 10* 
T2 



and T=Ti-T2 = Ti(l 



107 



in which A' = .0076/^; / being coefficient of friction and ^ the 
angle of contact of the belt in degrees. The formulas are derived 
on the assumption that / varies only with the normal force of 
contact and that centrifugal force on the belt is negligible. 
For belt speeds over 2500 ft. per min., centrifugal force must be 



36 FRICTION TESTERS 159 

considered. Its effect is to lessen the normal force between belt and 
pulley, thus decreasing the effective force, and 

-^.--('■.-^)('-ii.). 

in which w is the weight in pounds of a strip of belt 1 in. long and 
full width; v, its velocity in feet per second; and g, the accele- 
ration of gravity. 

In usual operation, there is always a certain amount of ^^ slip '' 
between the belt and the pulle^^s. Instead of running at the 
same linear velocity of points of contact, there is a relative 
velocity difference between the belt and each pulley rim. This 
fact invalidates to some extent the formula giving the relation 
between the belt tensions, since friction varies with the velocity 
of rubbing. Furthermore, so little is definitely known about 
solid friction, that the assumption F =fN is of doubtful accuracy. 
It is very likely that, in the case of belts, the coefficient of fric- 
tion / varies with the normal force N as well as with the velocity 
of slipping. As the formula depends upon an opposite assump- 
tion, results of the coefficient of friction obtained from it must 
be considered of very questionable value. On the other hand, 
we have no better formula, and for this reason it must be used. 

Belt-testing machines are instruments for testing the efficiency 
of transmission, for determining the slip under given conditions, 
and for determining the coefficient of friction. 

The efficiency of transmission may be found by measuring 
the power delivered to the belt wnth a transmission dynamom- 
eter and the power delivered to the follower pulley by an 
absorption dynamometer (see Fig. 74), suitable allowance being 
made for the friction of the shaft bearings. The difference between 
these quantities is the losses, which are due to work done by 
friction in moving through a distance equal to the slip and the 
work done in flexing the belt, windage neglected. 



160 FRICTION TESTERS 36 

The slip may be ascertained by counting the R.p.m. of the 
shafts; the difference between ^the linear velocities of the pulley 
rims is the total slip. The slip over either pulley may be found 
independently by measuring the linear velocity of the belt. 
This may be done by counting the number of times a chalk 
mark on the belt appears in a given time or by arranging a piece 
of metal to project from the edge of the belt so as to trip a 
revolution counter. Slip should be expressed in per cent of the 
driving pulley rim speed. Some forms of belt-testing machines 
have a differential gear arrangement by which the per cent 
cf slip may be directly read. 

To test for the coefficient of friction, apparatus must be pro- 
vided for the determination of the belt tensions, Ti and T2, 
so that the formula may be solved for /. This is usually done 
by separate measurements of the sum and difference of the belt 
tensions; adding these results and dividing by two gives Ti, 
knov.'ing which, To is readily obtained. 

The turning force of the belt, 7", equals the difference of 
the tensions. The moment of this turning force equals the torque 
shown by the friction brake (Fig. 74). Therefore, the difference 
of belt tensions may be calculated by dividing the torque sIioavti 
by the brake by the radius of the follower pulley. This radius 
should be m.rasured to the center line of the belt. 

To get the sum of the belt tensions, not including that due to 
centrifugal force, one type of machine has the driver pulley 
mounted freely on one arm of a bell-crank lever the other arm 
of which bears on a platform scales. The belt pull is then 
indicated on the scales in inverse proportion to the lever arms. 
Another t^'pe of machine has the belt arranged vertically, the 
follower pulley lacing freely suspended. The sum of the belt ten- 
sions is then equal to the weight of the follower pulley and 
attachments together with any additional weights used for the 
purpose of increasing the belt tensions. In both types, the total 
tension may be varied. 



36 FRICTION TESTERS 161 

The coefficient varies markedly with the condition of the 
rubbing surfaces, so every precaution should be used to keep 
this and other controllable conditions constant. The coefficient 
also varies with the humidity of the surrounding atmosphere; 
it is therefore well to make observations of this. 

(a) The Constants of the Instrument are those of the Prony 
brake (see Test No. 6) and of any lever arms used for getting the 
tensions. These are readily obtainable by direct measurement. 

Problem 36i. The torque as shown by the friction brake is 100 Ib.-ft. 

If the follower pulley is 2 ft. in diameter, w^hat is the difference between the 
belt tensions? If the sum of the belt tensions is 200 lbs. and the angle of 
contact is 190°, what is the coefficient of friction? Ans., /=0.33. 

Problem 36> Describe how a test should be made to show the variation 
of the coefficient with slip, all other conditions being constant. 

Problem 863. Describe how a test should be made to show the variation 
of the coefficient with the normal force of contact, shp and other conditions 
being constant. 



PART TWO 

THE ANALYSIS OF COMBUSTION 



THE CONSTITUENTS OF FUELS 

The principal commercial fuels are coals, oils, and gases 
in their various forms. The elemental constituents of these 
fuels, which for the most part are common to all of them, are 
carbon, hydrogen, oxygen, nitrogen, and sulphur. Of these 
constituents the ones depended upon to yield heat through com- 
bustion are carbon and hydrogen. Sulphur has a heat value, 
but it is an undesirable element in fuel since in coal it goes to 
form clinker and in gas it may combine with water to make 
sulphuric acid, these processes accompan}'ing the combustion of 
the fuel. Nitrogen and carbon in the form of CO2 are inert gases 
and are valueless to combustion. 

Carbon and hydrogen occur free or in combination with each 
other as hydrocarbons or in combination with oxygen. The 
only combustible carbon-oxygen compound is carbon monoxide, 
which is one of the most important of fuel gas constituents. 

Coal may be classified broadly as anthracite, semi-anthracite, 
semi-bituminous and bituminous, distinguishable by the amounts 
of so-called *' volatile matter '^ they contain. This is burnable 
material, mainly hAxIrocarbons, which may be driven from the 
coal without ignition. The usual percentages by weight of vola- 
tile matter in the '' combustible '' of the four classes of coal 
are given in the following table, which also shows the amounts 

162 



37 



CONSTITUENTS OF FUELS 



163 



that are left of carbon (referred to as '^ fixed carbon '^) when the 
volatile matter is driven off. By ^' combustible '' is meant the 
volatile matter and fixed carbon, leaving out of consideration 
ash and moisture. 



PROXIMATE ANALYSES OF DRY COMBUSTIBLE 




Anthracite. 


Semi-anthra. 


Semi-bit. 


Bituminous. 


Volatile matter 


3 to 7.5 

5 

95 


7.5 to 12.5 
10 
90 


12.5 to 25 
19 
81 


25 to 50 


Volatile matter, average . 
Fixed carbon 


37.5 

62.5 







The ash from coals is the residue when the combustible parts 
have been burned, and consists of such materials as clay, sand, 
slate, etc. The ash does not vary with the class of the coal, 
and may be widely different in proportion and quality in each 
of the classes. Water is also contained in coals, the amount 
varying with atmospheric and storage conditions. 

It should be observed that anthracite coal is mainly carbon 
and ash, there being generally very little volatile matter. 

A complete chemical analysis of a coal is called its ^^ ultimate 
analysis.'' The following table is for representative samples of 
the American product, and gives percentages based on the com- 
bustible. 

ULTIMATE ANALYSES OF COALS 





Anthracite. 


Semi-anthra. 


Semi-bit. 


Bituminoiia. 


Carbon 


95 

2.0 
0.8 
2.0 


90.5 
5 

'4' 


87 
5 

1.5 
4 


81 


Hydrogen 


6 


Nitrogen 


1 5 


Oxygen 


7.5 







When such an analysis is required it should be obtained from a 
chemist, as the methods and apparatus are remote from mechanical 



164 CONSTITUENTS OF FUELS 37 

experimentation. An analysis yielding the percentages of mois- 
ture, volatile matter, fixed carbon and ash, however, may readily 
be made by the skilled engineer, and often serves all the purposes 
in the study of combustion. This analysis is called the '^ proxi- 
mate analysis.'^ 

The kind of coal and its properties as fuel are determined 
roughly by the locality at which it is mined, but it should be 
noted that they may vary markedly in samples even from the 
same mine. 

The commercial grades of coal with relation to size are as 
follows, being listed in the order of the size, largest first. 

ANTHRACITE SIZE, INS. BITUMINOUS 

Broken 4 Run of mine 

Egg 3 Lump, various sizes 

Stove 2 Nut, various sizes 

Chestnut 1 j " Screenings, various sizes 

Pea I Washed sizes 

Buckwheat, No. 1 Ye 

Buckwheat, No. 2 I 

Buckwheat, No. 3 | 

Oils used for fuel are composed of different hydrocarbons 
of the form CnH2n-f2 or Cn-Hn, which have a wide range in such 
physical properties as specific gravity, volatility, burning and 
flash points. Gasoline and kerosene are the lighter distillates 
from crude oil. 

The percentages by weight of carbon and hydrogen in various 
fuel oils and their distillates from all parts of the w^orld are not 
very different. Carbon is generally between 83 and 87 per cent 
and hydrogen between 11 and 15 per cent, the rest being oxygen, 
nitrogen and sulphur. 

Gases. The principal gases used for fuel are illuminating 
gas, producer gas, natural gas, and blast furnace gas. The 



37 



CONSTITUENTS OF FUELS 



165 



following table gives the percentages by volume of the constituents 
of representative American gases. 

CONSTITUENTS OF GAS FUELS FOR POWER 

" Low " means less than 1 ner cent. 



Carbon monoxide, CO .... 

Hydrogen, H2 

Methane, CH4 

Ethylene, C2H4 

Benzol, CeHe 

Heavy hydrocarbons 

Oxygen, O2. 

Sulphureted hydrogen, H2S . 

Sulphur dioxide, SO2 

Carbon dioxide, CO2 
Nitrogen, N2 



Producer. Illuminatinf 



25 

12 

2 

low 

low 

low 

5 
55 



15 
45 
25 



1 
low 



Natural. 



low 

2 

95 

low 

low 
low 
low 

9 



Blast furnace gas is combustible mainly through CO. It 
contains a little hydrogen and methane, and is high in nitrogen. 

Analysis of these gases must be made by a chemist, with the 
exception, possibly, of producer gas and blast furnace gas. These 
may be analyzed by the Orsat apparatus (Test No. 40) if a pipette 
for the determination of hydrogen is provided, methane being 
ignored. 

37. The Proximate Analysis of Coal 

Sampling. When an analysis of a small sample is made to 
represent a large amount of coal, every precaution should be taken 
to secure a truly representative sample. For the purposes of 
boiler and producer tests, this may be done as follows. 

As each barrowful or charge of coal is removed from the pile 
for firing, an amount varying between a handful and a shovelful 
is withdrawn and put in a closed receptacle to make up a gross 
sample. The quantity of coal in each of these samplings and of 



166 CONSTITUENTS OF FUELS 37 

the gross sample necessary for accurate results depends upon 
the lump size of the coal, upon its homogeneity, and to a limited 
extent upon the total amount used. For the smallest sizes of 
coal of fairly uniform ciuality, the gross sample may be no more 
than 100 lbs.; under other conditions, it need not exceed 
250 lbs. Assuming 200 lbs., the gross sample is broken on a 
clean surface, preferably a piece of sheet iron, with the assistance 
of a tamping bar or weight, so that the largest lumps are not 
more than ^ in. diameter. This coal is then mixed and piled 
in the form of a cone. The cone should be ^' quartered '' into 
four heaps by passing a board through the cone axis in two planes 
at right angles. Tw^o diagonally opposite heaps are then dis- 
carded and the remaining two mixed, broken to | in., coned and 
again quartered. The process of quartering and discarding should 
he repeated until about 5 lbs. of coal lumps not larger than ^ 
inch are left. Half of this may be put aside in a sealed glass jar 
for check determinations if desired; the balance is to le run 
through a coffee mill or other crusher adjusted so that the lumps 
are reduced to about yq ^^- ^^^d less. After this has been thor- 
oughly mixed, a sufficient quantity of it for the proximate analysis 
is crushed by hand \vith mortar and pestle until all of that quan- 
tity is of such lump size as to pass through a sieve of 20 meshes 
to the inch. This last amount is used as follows. 

(a) Determination of Moisture, Volatile Matter, fixed Car- 
bon and Ash. About 5 gms. of the jt in. sample are carefully 
weighed before crushing in the mortar. After crushing, it is 
spread out on a large watch-glass, care being taken that no fine 
dust adheres to the mortar or pestle, and placed in a gas oven 
where it is kept at a temperature of 220° to 230° F. It is then 
placed in a desiccator to cool so that no moisture may be absorbed 
from the air. AMien cool enough to weigh accurately, it is covered, 
removed from the desiccator and weighed. It is then returned 
to the oven and left for a half hour, and the cooling and weigh- 
ing processes repeated. This is continued until the coal shows 



37 CONSTITUENTS OF FUELS 167 

no further decrease in weight. The difference between the first 
weight and the last is the weight of moisture. The percentage 
is figured on the basis of the weight of the sample including 
moisture. 

The gross sample may lose some of its surface moisture dur- 
ing the processes of quartering and crushing, by evaporation to 
the air. To avoid this as much as possible, reduction of the gross 
sample should be performed in a cool room in which the atmos- 
phere is neither very dry nor very moist, and it should be accom- 
plished as quickly as possible. 

To determine volatile matter, about 1 gm. of the coal is 
pulverized to pass through a 60-mesh sieve, having been pre- 
viously weighed. It is then placed in a covered crucible and put 
in the hottest part of the flame of a Bunsen burner which is 
8 ins. in height when burning free. After seven minutes, it is 
removed, cooled in a desiccator, and weighed. The difference 
in weight of the sample before and after heating equals the sum 
of its moisture and volatile matter. Knowing the former, the 
latter may be readily calculated. 

In this determination, it is important to exclude air from 
the crucible as otherwise some of the fixed carbon may be driven 
off as CO2. Some experimenters prefer to wet the coal after the 
first weighing so that the steam generated will displace the air 
in the crucible before the distillation of the volatile matter. 

Fixed carbon is found by subjecting the residue from the last 
test to the heat of a blast flame, the cover of the crucible being 
removed. Occasional stirring with a platinum wire assists 
combustion. It is generally a lengthy process to consume all of 
the fixed carbon; it may be hastened by directing a gentle stream 
of oxygen from a c^dinder filled Vvith that gas into the crucible. 
When the carbon is all burned, its amount is ascertained by 
cooling the sample in the desiccator, and weighing as before. 

The ash is determined by weighing the residue from the last 
test. 



168 CONSTITUENTS OF FUELS 37 

Sulphur, which occurs both in the volatile matter and in the 
ash, is sometimes separately analyzed for in the proximate 
analysis. 

To shorten the total time necessary for the proximate analysis, 
it is recommended that the tests for volatile matter, fixed carbon, 
and ash be made during the time that a separate sample is being 
dried out for the moisture determination. These tests will show 
volatile matter and fixed carbon plus moisture; allowance for 
the latter may be m.ade afterwards. 

(b) Calculation of Hydrogen and Volatile and Total Car- 
bon from the Proximate Analysis. For the complete analysis 
of boiler and producer performance, it is necessary to know 
the percentage of total carbon in the fuel and of hydrogen 
in the volatile matter. As the proximate analysis shows only 
the fixed carbon, that in the volatile matter may be estim.atcd 
and added to the amount of fixed carbon to get the total. 
Professor Lionel S. IMarks provides an empirical method cf 
doing this and of estimating the hydrogen in the volatile m.attcr. 
He has pointed out a relation applying to American coals by 
means of curves,* and these curves have been expressed, in part, 
by the following equations due to Professor Diederichs: 

Let /?c = hydrogen, exclusive of that in moisture; 

Cc = carbon in the volatile matter or ^S^olatile carbon"; 
z'c= volatile matter: 

all expressed a. weight-percentages of the combustible. Then 

Cc =0.02vc^ or OMvc - 10) for anthracites; 
Cc = 0.9(rc — 14) for bituminous coals. 
* rawer, Dec, 1908. 



37 CONSTITUENTS OF FUELS 169 

As an example of the use of these formulas, take the proxi- 
mate analysis given on page 270, and let it be required to find 
the hydrogen in one pound of the coal, Ht, and the total car- 
bon, Ct. 

The combustible, being the sum of the fixed carbon and 
volatile matter, is .807 + .0617 =0.869 lb. per lb. of coal. 
Hence 

Vc = ' Q^f. X 100 -7.1 per cent, 

and 

hc = 7.l L^^^^^ -0m3\ =3 per cent. 

This is the percentage of hydrogen based on the combustible. To 
base it on the coal, we have 

Hi = yfo X0.869 = .026 lb. of hydrogen per lb. of coal. 

Similarly for the volatile carbon, 

Cc = .02X7.l2 = l per cent. 

Consequently in 1 lb. of coal, there is j^^X -869 =.00869 lb. of 
volatile carbon, and the total carbon is 

C, = . 8:7 + .00869 = .816 lb. 

Problem 37i. The proximate analysis of a coal gives moisture = 1 per 
cent, volatile matter =22, fixed carbon = 72, and ash =5. What are the 
percentages of hydrogen and carbon in the volatile matter, and what is the 
percentage of total carbon? Base answers on coal as analyzed, not on com- 
bustible. Ans., 4.6, 8.5, 80.5%. 

Problem 372. Give the proximate analysis in the preceding problem 
-^n the basis of " dry '' coal instead of coal " as received.'^ 

Arts., 1.01%, etc. 



170 HEAT VALUE OF FUELS 38 

THE HEAT VALUE OF FUELS 

When used for the generation of power, combustion may be 
defined as the rapid chemical combination of the oxygen in air 
with the combustiljle constituents of fuel, which combination 
is accompanied by the evolution of heat. It has been pointed 
out that the elemental combustibles in fuels are carbon, hydrogen, 
and to a lesser degree, sulphur. The complete combustion of 
carbon forms carbon dioxide, CO2, and of hydrogen, water, H2O. 

When a unit mass of fuel is burned completely, the heat 
evolved raises the temperature of the materials entering into 
the combination and of surrounding objects. If the products 
of combustion are cooled to the temperature before combustion, 
then the total heat given up is the *' heat ^' or ^' calorific value '^ 
of the fuel. Or, more briefly, the heat value of a fuel is the number 
of heat units that ore released by the complete combustion of a unit 
mass of the fuel. 

It should be noted that to release all of the heat generated, 
the products must be cooled down to room temperature. This 
may be done in two ways, namely, so that the H2O formed by 
combustion of the hydrogen remains as steam or so that the 
H2O is condensed. In the former case the latent heat of the 
steam remains in the products of combustion, the heat released 
is correspondingly less, and is referred to as the ^' lower heat 
value. ^' In the latter case the latent heat of the steam is included 
in the heat released which is then called the ^^ higher heat value.'' 

Whether the one or the other quantity should be used depends 
upon the character of the test for which the heat value is needed. 

The difference between the two values depends upon the 
amount of hydrogen in the fuel. For coals, it is comparatively 
small, but for gases and oils it may be as high as 15 per cent. 

The units in which heat values are expressed in the United 
States are as follows, corresponding French units being used 
to a limited extent only. 



L 



38 HEAT VALUE OF FUELS 171 

For solids, B.t.u.s per pound. 

For liquids, B.t.u.s per pound or per gallon. 

For gases, B.t.u.s per standard cubic foot. 

The standard cubic foot of gas is a cubic foot of gas under 
standard conditions of pressure and temperature. That this 
specification is necessary will be seen when it is considered that 
the mass of gas in a cubic foot depends upon these conditions, 
and consequently its heat value. The standard conditions 
of pressure and temperature are either 29.92 ins. of mercury 
and 32° F., or 30 ins. of mercury and 62° F. These pressures 
are the same and equal to 14.7 lbs. per square inch, the difference 
in the mercury columns being due to the temperature differences. 

In this work the 32 degrees standard will be used. 

The following gives experimentally determined heat values 
of the elemental combustibles and of various gases, and of fuels. 

HEAT VALUES IN B.T.U. PER POUND 

Carbon burned to CO2 14,600 

Carbon burned to CO 4,400 ' 

Sulphur burned to SO2 4,000 

XT . . XT r^ f 62,000, higher 

Hydrogen to H^O j^^isoo! lower 

HEAT VALUES IN B.T.U. PER STANDARD CUBIC FOOT (32°) 

Higher. Lower. 

Carbon monoxide, CO 342 .... 

Hydrogen, H2 346 294 

Methane, CH4 1065 955 

Ethylene, C2H4 1680 1560 

Benzol, CeHg 4000 3830 

HIGHER HEAT VALUES OF COMMERCIAL FUELS, B.T.U 

Coals 11,000 to 15,000 (per lb.) 

Oils 18,000 to 20,000 

Illuminating gas, average 650 (per cu. ft.) 

Producer gas " 150 '' 

Natural gas " 1050 '' 



172 HEAT VALUE OF FUELS 38 

If it is desired to refer the heat values of the gases to the 
62 "^ standard, it is only necessary to multiply by 0.943, the 
ratio of absolute temperatures. 

Instruments for determining the heat value of fuels are called 
^' fuel calorimeters/^ 



38. The Determination of the Heat Value of Coal 

Principles. This may be done by calculation from empirical 
formulas involving the results of the proximate or ultimate 
analysis of the coal, or by the use of a fuel calorimeter. The 
latter method is the more accurate. 

Results from coal calorimeters are obtained by burning a 
small sample of the coal in an air-tight chamber immersed in 
water. The heat given up to the water and calorimeter parts 
by the combustion of this coal is measured by the rise of tem- 
perature, from which the heat value of the coal may be 
calculated. 

The essential parts of a coal calorimeter are the water 
vessel, jacketed to prevent radiation, the combustion chamber 
or ^^ bomb ^' with a device for igniting the charge, and a ther- 
mometer or its equivalent. Ignition is accomplished either by an 
electric current or by dropping a bit of white hot wire through a 
tubeinto the bomb, a valve being arranged to allow its entrance and 
to prevent the exit of the gases generated. To support combustion, 
oxygen is charged with the coal, either in the free state from a 
cylinder under pressure, or in the form of a chemical rich in oxygen. 
One of the most convenient of these instruments is the Parr 
calorimeter, with which sodium peroxide is used as a source of 
oxygen. 

Sampling of the coal to be tested should he done exactly as 
for Test 37, except that the last crushing should be to particles 
that will pass through a 100-mesh sieve. The final sample should 



38 HEAT VALUE OF FUELS 173 

be dried in an oven at 220^ to 230° F. before it is charged in 
the calorimeter. 

(a) Determination of Heat Value by the Parr Calorimeter. 

Let W stand for the weight of water used in pounds, w, the water 
equivalent of the bomb, water vessel and parts (that is, the weight 
of water that would absorb the same amount of heat in the same 
temperature range), and T, the temperature rise brought about 
by the combustion of C lbs. of coal mixed with the appropriate 
weight of sodium peroxide. The heat given up by the com- 
bustion is then (W+w)T, Now, 27 per cent of this heat is due 
to the by-reactions of the sodium peroxide, so that there remains 
an amount equal to 0.73 (TF+'?^)T' generated by the coal. There- 
fore, the heat value of the coal is 

.73{W+w)T 



The water equivalent, v:, may be taken as 0.3. Generally 2 
liters of water and | gram of coal are used. In English units, 
these weights are 4.41 and 0.001102 lb. Combining the con- 
stants, we have 

Heat value = •'^^^^-^|+^-^V = 31177-. 

The temperature T is the observed temperature minus cer- 
tain corrections. The hot wire adds some heat which should be 
allowed for by subtracting 0.022° F., from the observed tem- 
perature. Anthracite coal is somewhat difficult to burn com- 
pletely in the bomb, so an additional chemical (about 1 gm.) 
called ^^ accelerator '^ is used, the heat from which should be 
allowed for. The accelerator consists of 2 parts by weight of 
potassium persulphate and one of ammonium persulphate. The 
corrections are 0.005 degree for each per cent of ash and 0.010 
for each per cent of sulphur, to be subtracted. 



174 HEAT VALUE OF FUELS 38 

Radiation from the calorimeter is very smalL It may be 
corrected for roughly by noting the fall in temperature imme- 
diately after the maximum temperature has been reached and 
during an interval of time equal to that between ignition and the 
occurrence of maximum temperature. The correction should 
be added to the observed rise. 

Radiation may be practically obviated by making the initial 
temperature of the water about 2° less than that of the room. 
As the observed rise in temperature is between 4 and 5° the 
radiation will be balanced. 

The procedure for the test is to add about 9 gms. of sodium 
peroxide to ^ gm. of coal, mix thoroughly in the bomb, 
ignite, and, during the period of heating, to revolve the bomb 
in the calorimeter so as to circulate the water. This last is 
accomplished by means of vanes attached to the bomb, the 
purpose being to quickly make the temperature of the water 
uniform. The temperature rise is noted from a finely graduated 
thermometer. 

Care should be taken not to allow water to touch the sodium 
peroxide, as they react violently. 

(b) Calculation of Heat Value from the Fuel Analysis. If 
the combustibles in coal were in the elemental form, it would be 
easy to calculate the heating effect from each according to its 
amount and thus get the heating value of the coal. This, how- 
ever, is not so; they are combined as hydrocarbons and other- 
wise. Now when combustion takes place some heat must be 
given up to the hydrocarbons to separate the carbon from 
the hydrogen so that they may recombine with oxj'gen. That 
is, some heat becomes latent through dissociation of the elements 
which lessens the heat availal^le from their combination with 
oxygen, ^o there is an interchange of heat in burning coal 
which makes its heat value dependent upon the previous com- 
bination of its elements. We therefore cannot calculate heat 
values with precision in this wa}', but certain empirical for- 



38 



HEAT VALUE OF FUELS 



175 



mulas enable us to make fair estimate?. One of them is Dulong's 
as below. 

Heat value = 14,600C+62,00cf^-g j +4000>S, 

the symbols C, H, 0, and S standing for the weights in pounds 
of carbon, hydrogen, oxygen, and sulphur in 1 lb. of the fuel, 
respectively. The result is in B.t.u. per pound. This formula 
uses the ultimate analysis of the coal, and is more applicable to 
anthracite than to bituminous coals. 

Another formula, using the proxim_ate analysis, is Goutal's.* 
This is 

Heat Yslue = K7.GXfc+KXvm, 

in which fc and vm are the percentages of fixed carbon and 
volatile matter in the fuel as received, respectively, and K has 
different values depending upon the amount of volatile matter, 
as shown in the curve, Fig. 75. 



260 
250 
?40 
250 
2Z0 
2iO 
200 
190 
180 
170 
160 
150 
140 
150 
120 
110 



kT 


\ 


V 




\ 


"^ 


^^ 


^^ 


^^^ 


"'^ 


\ 


\ 


jr 


I 


jt 



10 12 14 16 18 20 22 24 26 Z8 30 32 54 36 38 40 42 
PERCENT VOLATILE MATTER IN FUEL AS RECEIVED 



44 46 



Fig. 75. 



Fig. 76 is a reproduction of IMahler's curve, from which, 
probably, may be had as reliable a result of heat value as any 

* Wisconsin Engineer, Dec, 1911. 



176 



HEAT VALUE OF FUELS 



38 



of the relations proposed for this purpose. As an example of its 
use assume a coal with 16.9 per cent of volatile matter and 70.8 
per c^nt of fixed carbon. Then 

Combustible in the coal =16.9+70.8 =87.7 per cent; 

Fixed carbon in the combustible =70.8-^87.7 =80.6 per cent. 




^^500- — ^ 65 jQ 75. 80 85 90 95 100 
Per Cent of Fixed Carbgn in Combustible 

Fig. 76. — Mahler's Curve for Coal Heat Values. 

From Fig. 76, against 80.6 per cent is found the heat value of 
the combustible, 15,800 B.t.u. per pound. Consequently, the 

Heat value of the coal =15,800 X. 877 = 13,900 B.t.u. 

It should be emphasized that all of these relations for calcu- 
lating the heat value of coal are approximate, and generally give 
better values with the lower percentages of volatile matter; the 
probable error then being within 2 per cent. 

Problem 38i. A sample of bituminous coal is tested for heat value. 
Ignition by hot wire. 2.5 liters of water used. Water equivalent of calo- 
rimeter =0.40 lb. Sample weighs 0.6 gm. How much heat is generated and 
what is the heat vahie if temperature rise is 4.23° F.? Ans., 13,300 B.t.u. 

Problem 38> Calculate the heat value of coal giving a proximate analysis 
as follows: moisture, 2.75; volatile matter, 6.00; fixed carbon, 78.45. Ash, 
12.8 per cent. Use Mahler's curve. What would be the heat value if the 
coal were drv? Ans., 12,900 and 13,300 B.t u. 



39 HEAT VALUE OF FUELS 177 

39. The Determination of the Heat Valle of Gases 

AND Oils 

Principles. The heat vahies of gases may be calculated 
readily from their chemxical analyses, but this is not true of oils 
on account of their complex structure. Both oils and gases may 
be tested for heat value by the use of a properly designed calo- 
rimeter. The Junker calorimeter is universally used for this 
purpose. 

This instrument is an ingenious arrangement of heating 
surfaces surrounded by water, by which all the heat generated 
by the fuel to be tested is passed to the water. The water is 
kept flowing through the calorimeter at a constant rate, secured 
by keeping it under a constant head, and enters continuously 
at a uniform temperature. Upon leaving the calorimeter, it 
m.ay be weighed, and the heat added ascertained by noting its 
rise of temperature. In order that all the heat be given up to 
the water, the products of combustion must return to the tem- 
perature of the fuel and air from which they came, before leaving 
the calorimeter. This is ascertained by a thermometer placed 
in the exit gas flue. The water resulting from the burning of 
hydrogen is condensed and collected, should it be desired to 
calculate the lower heat value. (See p. 170.) 

For gases, a Bunsen burner is used and a small gas m.eter to 
measure the fuel in cubic feet. For liquid fuels, a special 
regenerative burner is used which, together with the lamp con- 
taining the fuel, is attached to one arm of a beam balance so 
that the weight of fuel burned ma}^ be measured at any time 
during the test. 

There is no water equivalent of the calorimeter to be con- 
sidered since, during operation, all parts are at constant tem- 
peratures. 

Radiation is provided against by air jacketing and polished 
surfaces, and is neghgible. 



178 HEAT VALUE OF FUELS 39 

Sampling. If the sample to be tested represents a gas used 
in a test of several hours' duration, it is best to take a continuous 
sample covering the whole time of the test as described on page 
193, for exhaust gas sampling. This involves rather a large 
gas container, however, and it is more convenient to draw the gas 
from the main directly into the calorimeter. For this purpose 
the main should be tapped at a point as near as possible to the 
place where the gas is used. Then, if a number of heat value 
determinations are made covering equal intervals of time and 
separated by equal intervals, their average will be the average 
heat value of the total gas delivered in the main. 

(a) Determination of Higher Heat Value. The rates of water 
and gas flow should be adjusted so that the temperature of the 
products of combustion upon leaving the calorimeter is that 
of the room. Then, if t and T are the temperatures of the 
water before and after heating, respectively, in degrees Fahrenheit, 
]r, its weight in pounds, and G, the cubic feet of gas burned, 
we may say 

Higher heat value= (^-OTF-^G. 

In this, G is the number of cubic feet of gas under standard con- 
ditions (see p. 170). To convert the gas meter reading into 
standard cubic feet, it is necessary to use the relation that the 
volume of a gas varies directly as its absolute temperature and 
inverse!}^ as its absolute pressure. Consequently, the pressure 
as well as the temperature of the gas should be noted. This 
involves a reading of the barometer and of a manometer set in 
the gas main. 

The heat value determined in this way is not quite the higher 
value, for the reason that not quite all the water of combustion 
is condensed. This is because the air entering combustion is 
not saturated with water vapor (although the fuel may be), 
but the products of combustion are saturated. Tlie difference in 
the humidities is due to the water of combustion which is 



39 HEAT VALUE OF FUELS 179 

not condensed. To avoid this error, it may be arranged to feed 
the calorimeter with saturated air and gas. The determinations 
as made without this precaution are acceptable for most purposes. 

(b) Determination of Lower Heat Value. This is determined 
correctly by subtracting from the heat added to the water the 
amount which came from the vapor in condensing, or its latent 
heat. To get this amount correctly, we should know the weight 
of the vapor and its latent heat per pound. The latent heat of 
steam is generally determined from its pressure by reference 
to the steam tables. In the case of steam mixed with other 
gases, the pressure of the steam is only partial (see p. 142) and 
therefore difficult to determine. Under the conditions existing 
during the operation of the Junker calorimeter, it is convenient 
and sufficiently accurate to take the latent heat of the steam 
as that corresponding to the temperature of the exhaust gases, 
that is, room temperature. Letting L stand for this heat and 
w for the weight of condensation, we have 

Lower heat value = ^ — ^ , 

the other notation being as used under (a). 

An average value of L may be taken as 1060 for temperatures 
between 50° and 70° F. 

(c) Calculation of the Heat Value from the Fuel Analysis. 
This maj^ be readily and accurately done in the case of gases when 
the complete analysis is known. The following rule may be 
used: 

To calculate the higher or lower heat value of a fuel gas, multiply 
the higher or lower heat value of each of the constituent gases, in 
B.tM, per standard cubic foot, by its volume percentage, as shown 
by the fuel gas analysis, and divide by 100. Add these results 
together; the sum is the desired heat value. 

The heat values of various constituents of fuel gases are 



180 PRODUCTS OF COMBUSTION 40 

given on page 171. An example of the calculation is given in 
columns 1, 2, 6 and 7 of the table on page 294. 

Problem 39i. Figure the higher heat value from a calorimeter test 
giving data as follows. Pressure of gas = 4 ins. of water. Barometer, 29.4 
ins.; temperature of gas, 70° F.; 7.24 lbs. of water raised from 60.7° to 
116.3°. Volume of gas burned, 0.875 cu. ft. by meter. Ans.j 500 B.t.u. 

Problem 392. In the preceding problem, if there were .048 lb. of water 
of condensation, what would be the lower heat value? Ans., 437 B.t.u. 

Problem SSa. Calculate the higher and lower heat values of the producer 
gas, analysis of which is given in the table on page 165. Ans., 148 B.t.u. 



THE PRODUCTS OF COMBUSTION 

The products of combustion of fuels used CDmmercially are 
called exhaust gases. By their analysis, we learn the completeness 
of combustion and the directions and amounts of heat losses in 
the operation of boilers, internal combustion engines, and gas 
producers. 

Commercial combustion, as previously defined (p. 170) 
involves the chemical comljination of the oxygen in air vith 
the combustibles of a fuel, resulting in CO2 and H2O. Air is 
principally oxygen and nitrogen, the other constituents being 
negligible in this analysis, and the proportions may be taken 
as 21 of oxygen to 79 of nitrogen by volume. Now, in order 
to secure complete combustion, it is necessary always to furnish 
an excess of air over tho amount required to convert all the 
carbon to CO2 and hydrogen to H2O. The exhaust gases will 
therefore contain free oxygen and nitrogen due to this extra 
air, in addition to CO2 and H2O. Sometimes the combustion 
is incomplete, in which case the exhaust gases may contain 
CO, free hydrogen, and hydrocarbons. With proper operation 
however, these are each less than 1 per cent by volume of the 
total exhaust . gases, and the hydrogen and hydrocarbons are 
almost always negligible. The experimental determinations 



40 PRODUCTS OF COMBUSTION 181 

are therefore generally only for CO2, CO, O2, and N2; H2O 
being calculated from the fuel analysis. The analysis of the 
exhaust gases is found and expressed as percentages by volume. 

The ratio, by volume, of the air actually suppUed to the 
fuel to that required for '^ complete theoretical combustion," is 
called the '^ excess coefficient. '^ 

The Principles Involved in the Applications of exhaust gas 
analyses depend upon Avogadro's law. It is important that this 
law be thoroughly understood. Following is a statement of it: 

In a given volume of any gas, there is always the same number 
of molecules, regardless of the nature of the gas, provided the con- 
ditions of pressure and temperature are constant. 

We therefore know that in a vessel containing a mixture of 
gases, there is the same number of molecules as though only 
one of them or of any gas existed there alone, irrespective of the 
number of atoms in the molecules. Also, the number of mole- 
cules in 2 cu. ft., for example, is twice the number in one; that 
is, the number of molecules in a gas is directly proportional 
to its volume. 

It follows from Avogadro's law that, for given conditions 
of pressure and temperature, the volume occupied by a single 
molecule of any gas is a constant quantity. Since all of the 
determinations from exhaust gas analysis are relative, it will 
be convenient to conceive this volume as a cubic foot and to 
use the unit, ^^ molecule-foot,'^ to express it. 

Elemental gases are supposed to have two atoms to a molecule. 
For that reason they are written O2, N2, H2, etc. Carbon 
does not occur as a gas except in combination with other elements, 
but it will be convenient to consider hypothetical gaseous carbon 
having a single atom to the molecule. 

The relative weights of the elements under consideration, 
compared with that of hydrogen (that is, their atomic weights), 
rro as follows. 

H = l, = 16, N = 14, C = 12 



..^^iM 



182 



PRODUCTS OF COMBUSTION 



40 



V 



?? 



oo 



•o 



Ni troofen 



« 



19 .t?. 



Carbon Dioxide 



V 



oo 



oo 



V 






oo 



V 



oo 



oo 



V 



^ 



oo 



oo 



•Carbon Monoxiole 

Fig. 77. 
Molecule-feet. 



cents of the 
per cent is a 
fcot contains 



The molecular weight of a gas equals the sum of the weights 

of the atoms in its molecule. Thus, H2 weighs 1 + 1=2, O2 

weighs 16 + 16-32, CO2 weighs 12 + 16+16 = 44, and so forth. 

As an illustration of the way in which these principles are 

applied, consider a mixture of gases consisting of 10 per cent of 

CO2, 1 of CO, 9 of O2, and 80 of N2; all 
per cents being by volume. Since these 
gases are expressed relatively (the basis 
of the comparison being 100 parts, i.e., 
per cent) we may consider their percent- 
ages as cubic feet, or as molecule-feet. 
Fig. 77 represents the per 
gases considered thus, each 
cubic foot and each cubic 
a single molecule. 

Suppose we wish to find the ratio by weight 
of the oxygen in the gas to the carbon. There are 9 molecule-feet 
of oxygen as such, 10 molecule-feet of oxygen in the form of CO2, and 
one-half a molecule -foot as CO, making a total of 19.5 molecule- 
feet. Since the molecular weight of O2 is 32, the total weight of O2 
is 19.5X32. Similarl}^ the number of molecule-feet of carbon 
is 10+1 = 11, having a weight of 11X12. Dividing the weight 
of oxygen by the weight of carbon, 19.5X32-^132, we get the 
desired ratio of weights, 4.72. Since this is a ratio, it may be 
expressed in any units of weight, for example, 4.72 lbs. f oxygen 
per pound of carbon. In this way we may figure the weight in 
pounds of any or all of the gases or of the elements composing 
them per pound of any of the constituents. 

The total carbon used in combustion may be measured when 
in the form of fuel. If this weight is multiplied by that of any 
of the products of combustion, expressed in pounds per pound 
of carbon, the result is the total weight of that product of com- 
bustion. This follows from the assumption that all of the carbon 
iji the fuel appears in the exhaust gas analysis. 



40 PRODUCTS OF COMBUSTION 183 

Theoretical Reactions of Fuels 

Products from Coal Combustion. In the burning of pure 
carbon, if complete combustion could take place with no excess 
of air, the reaction would be 

79N2+2IO2+2IC-2ICO2+79N2 

showing that the exhaust gas would consist of 21 per cent of CO2 
and 79 per cent of N2. Now, if more than this amount of air is 
used, the sum of the free oxygen and of the CO2 in the exhaust 
gas will bear the same relation by volume to the nitrogen as the 
oxygen did in the air, since the volume of the oxygen is not 
increased by combination with carbon. Consequently the sum 
of O2 and CO2 is 21 per cent, and N2 is again 79 per cent. 

Ash does not vary this relation, but the effect of hydrogen, 
oxygen, and nitrogen in the coal is to alter it. The last two have 
slight effect, but the hydrogen needs oxygen from the air to burn 
to water, and as the water does not appear in the exhaust gas 
analysis, a corresponding amount of oxygen disappears. This 
increases the percentage of nitrogen. The formation of CO 
instead of CO2 has an opposite effect, since the oxygen entering 
the combination makes twice the volume of CO* on the other 
hand CO is generally low. 

Anthracite and semi-anthracite coals, being low in hydro- 
gen, will yield exhaust gas having between 79 and 80 per cent 
of N2. Bituminous coals will yield between 80 and 81.5 per 
cent. Results outside of these figures are questionable. 

It is obvious that the less air is used, the less will be the free 
oxygen in the exhaust gas, and the greater will be the CO2. It 
will be shown (Test No. 54) that the less the air used the more 
economical is the combustion, provided that there is not so little 
air as to cause material loss from incomplete combustion. Con- 
sequently high CO2 is a desirable indication. 



184 



PRODUCTS OF COMBUSTION 



40 



Fig. 78 shows the variation in the products of combustion 
of carbon and of sohd fuels, for ^ arious amounts of air, assum- 
ing complete combustion. 

Products of Oil Combustion. Since the proportions of the 
elemental coni-tituents of fuel oils a:e approximately constant for 
all of them, the products of their complete combustion will also 
be constant under the sa:::e conditions of air supply. An average 
analysis is C, 84, and II2, 1-i per cent by weight. The ratio of 



PRODUCTS OF COMBUSTION FROM FUELS 



E 



^15 



[Carbon > 
\Anfhracife 

'^Bifuminouz —— 1 



lie 



k 












^^0, 










^"^?$4^^^*-— 


y 


^ 




' — «>«^ 


^ 


/ 























"^ 










1 












^, 






i>- 


>< 


■^ 


/ 









Producer Gon 
Illuminating 5^j4— — |— 






1 




















^ 




oJ 


^ 


<c 


^ 













1 1.25 1.50 1.75 2.00 ^25 1 1.25 1.50 1.75 1 1.25 L50 1.75 2.00 2.25 

Excess Coefficient 



Fig. 78. 



Fig. 79 



Fig. 80. 



volumes of carbon to hydrogen in molecule-feet is 84-^ 12 to 14-^2 
or 1 to 1. xVs it takes 100 molecule-feet of air to burn 21 of car- 
bon to CO2, and half that much to burn an equal amount of hydro- 
gen to H2O, the following will be the reaction assuming no excess 
air and complete combustion. 



158X2+42O2+42C + 
79N2+2102+42H2 = 237X2+42C02+42H20. 

As the H2O disappears, the total volume of the products of com- 
bustion is 237+42 molecule-feet. This divided into 42 gives the 



40 PRODUCTS OF COMBUSTION 185 

percentage of CO2, about 15 per cent. This is the maximum 
value in the exhaust gas from usual oil fuels. 

Fig. 79 shows the variation in the exhaust gas from oils for 
various amounts of air supplied. It should be noted that in the 
case of internal combustion engines, oil or oil vapor has a limited 
range of explosibility so that the excess of air cannot be very high. 
If the proportions of the exhaust gases are markedly different 
from those shown by Fig. 79, the CO2 being low, it is probable 
that incomplete combustion is taking place and that hydro- 
carbons are appearing as N2. 

Products of Gas Combustion. The proportions of hydrogen 
and carbon in the different fuel gases vary w^idely and this causes 
wide variations in the exhaust gases. Furthermore, some of the 
fuel gases contain high percentages of nitrogen, which makes 
that gas correspondingly high in the exhaust, and the CO2 low. 
Knowing the analysis of a given fuel gas, the number of molecule- 
feet of C, H2, O2, and N2 may be readily counted, from which 
the theoretical reaction may be figured as for oil. A convenient 
method of counting the molecule-feet is shown in the table, 
p. 294, under columns 3, 4, and 5. 

Fig. 80 shows the variation in the products of comtustion 
of representative producer gas and of illuminating gas, for various 
amounts of air, assuming complete combustion. 

Calculation of the Exhaust Gas Analysis to be Expected from 
a Given Fuel. It is often advisable to make such calculations in 
order to check the actual analysis obtained by experiment. 

Let c, hj Qj and n be the number of molecule-feet of C, H2, 
O2, and N2, respectively, in 100 molecule-feet of the fuel. The 
analysis of solid and liquid fuels gives the percentages of these 
elements by weight; dividing the percentages by the molecular 
weights of the elements, respectively, gives the number of mole- 
cule-feet. Analyses of gases give percentages by volume; the 
molecule-feet may be counted as in columns 3, 4, and 5 of the 
table on page 294. Let X be the ratio by volume of the air 



186 PRODUCTS OF COMBUSTION 40 

supplied in the actual combustion to the air needed as shown by 
the theoretical reaction, that is, the excess coefficient. 

Since there are c molecule-feet of carbon in the fuel, there 
will be c molecule-feet of CO2 in the exhaust. Since carbon 
requires 1 molecule-foot of O2, and h3'drogen half as much, for 
complete combustion, the amount of oxygen needed is c+0.5/i. 
But the fuel furnishes g molecule-feet of O2. There will then be 
(X — l)(c+0.5/i — gf) molecule-feet of oxygen as excess which will 
appear as free ox^^gen in the exhaust gas analysis. The nitrogen 
accompan\'ing the oxygen supplied as air is |fX(cH-0.5/i — g). 
In addition to this nitrogen, there will appear in the exhaust n 
molecule-feet of nitrogen from the fuel. Adding all these volumes 
gives the total volume of the products of combustion in mole- 
cule-feet, which, simplified, is 

c+(4.75X-l)(c+0.5/i-g)4-n. 

Calling this T, we have for the volume percentages of the 
exhaust gases, 

%CO2 = 100c-^r 

%O2 = 100{(X-l)(c-f0.5/i-^))-y 
%N2 = 100{3.75X(c+0.5/i-^)+n}-7-r 

Nitrogen may also be obtained b}' subtracting the percentages 
of CO2 and O2 from 100. 

As an example in the use of these formulas, consider the 
combustion of the producer gas the analysis of which is given 
on page 165, assuming the excess coefficient to be 1.5. Count- 
ing the molecule-feet, we have 

c = 25+2+5 = 32 
/i = 12+4 =16 
^ = 12.5+5 =17.5 
n= 55 



40 PRODUCTS OF COMBUSTION 187 

from which, r = 32+(4.75Xl.5-l)(32+0.5Xl6-17.5)+55 
= 225 

and %CO2 = 100X32-^225 = 14.2 

%O2 = 100{ (1.5- 1)(32+0.5X16- 17.5) }-f- 225 

= 5.0 
%N2 = 100 -14.2 -5.0 = 80.8 

It should be remembered that these percentages are what 
would result under complete combustion; the actual percentages 
will be somewhat different if this condition does not obtain, 
as would be indicated by the appearance of CO in the exhaust. 

It is convenient to express the corresponding formulas for 
coals and oils in terms of their constituents by weight, since 
the fuel analyses are so expressed. Let C and H stand for the 
weights of carbon and hydrogen per pound of fuel, respectively. 
The other constituents may generally be neglected, since in the 
fuels considered they have but small effect upon the exhaust 
gases. Now C-t-12 and //-^2 are proportional to c and h, 
respectively. Substituting these values for c and h in the equa- 
tions for gas fuel combustion, and neglecting n and g^ we have, 
for coals and oils, 

100 C 



%C02 = 
%02 = 



C+(4.75Z-l)(C+3i?) 
100(X-1){C+3H) 



C+(4.75X-l)(C+3i/) 
%N2 = 100 - %C02 - %02 

If the analysis of a fuel to be used during a test is approx- 
imately known, it is often of value to calculate the exhaust gas 
analysis to be expected from it using different amounts of air, 
and to plot the results as curves similar to Figs. 78, 79, and 80. 
By comparing the actual results of the analyses during the test 



188 PRODUCTS OF CO:\IBUSTION 40 

with those shown by the curves, their correctness may be roughly 
checked; and, when hydrocarbons appear as nitrogen, their pres- 
ence may be deduced. 

Air Required for Complete Theoretical Combustion, per 
Pound cf Fuel. This is the amount that would be used if com- 
plete combustion could occur without excess of air. For coals 
and oils, it is convenient to express it in pounds of air per pound 
of the dry fuel. 

A molecule of oxygen, weighing 32, unites with 1 of carbon, 

weighing 12, to make CO2. Consequently there will be H lbs. 

of O2 used for every pound of C })urned. As oxygen is 23 per 

cent l>y weight of the air containing it, the air required to burn 

32 

each pound of C is ■ lbs., or 

^ 12X.23 

11.6 lbs. of air to burn 1 lb. of C. 

Two molecules of hydrogen, weighing 4, unite with 1 of O2 
to make H2O. Consequently there will be 4- -^.23 lb. of air 
required to burn each pound of H2, or 

34.8 lbs. of air to burn 1 lb. of H2. 

If C and H stand for the weight of carbon and hydrogen in one 
pound of the fuel, and it the fuel contains no oxygen by which 
combustion may be supported, then the total amount of air 
needed per pound of fuel is 11.6C+34.8//. If the fuel con- 
tains Us. of oxygen per II3., a corresponding amount less of air 
is needed, namely ^0 = 4.35 0. In the general case, then, 

Air required = 11.6C+34.8^-4.3o lbs. per lb. fuel. 

For Gas Fuels, the air required is generally expressed in cubic 
feet of air per cubic foot of fuel, the conditions of temperature 
and pressure being the same for both. 



40 PRODUCTS OF COMBUSTION 189 

Letting c, /i, and g stand for the number of molecule-feet 
of C, H2, and O2, in 100 molecule-feet of the fuel, counted as in 
columns 3, 4, and 5 of the table on page 294, there will be required 
c molecule-feet of O2 to burn the C to CO2, and 0.5 h molecule- 
feet of O2 to burn the H2 to H2O. Since there are g molecule- 
feet of O2 contained by the fuel, only {c+0,5h — g) molecule-feet 
of O2 will be required from the air to burn 100 molecule-feet 
of the fuel. Therefore, 

Air required^- ' ' cu. ft. per cu. ft. fuel. 
xUU /\ .^ i 



40. The Analysis of Exhaust Gas 

Principles. The gas analysis apparatus depends upon the 
separate absorption of the products of combustion by certain 
reagents. A measured volume of the gas is brought into contact 
with one of these reagents which removes the CO2, but does not 
take up any of the other constituents. The CO2 is then deter- 
mined by measuring the diminution in volume. In this way 
the volumes of CO and O2 may also be found. The residue is 
assumed to be N2. It is convenient to make the original volume 
100 units, as cubic centimeters, in which case the differences 
are per cents. 

The Orsat apparatus in its various forms is in general use for 
engineering analj^ses of exhaust gas. It consists of a measuring 
flask, jB', called the burette (see Fig. 82), a distributing tube, 
T, and three so-called pipettes, DD\ 00' , and MM\ containing 
the reagents. The gas sample is displaced from the burette 
into each pipette in turn by filling the burette with water from 
the bottle B, The right leg of the pipette is completely filled 
with reagent just before the gas enters; the gas displaces it into 
the left leg. Rubber bags, /?, seal the left legs of the pipettes 



190 



PRODUCTS OF COMBUSTION 



40 



so that the reagents will not deteriorate through contact with the 
atmosphere. 

If desired, the apparatus may be provided with a fourth pipette 
for determining hydrogen. 

There are many other types of exhaust gas analysis apparatus, 



^amplincf Tube 



Rubber Tube 




* Jm/m//////////////////^^^>r ^ 



Fig. 81. — Gas Sampling 
Bottle. 



To F 




^ 



M' 
K 


M 
K 











r 1 


\-~ ■ -J 




y\ 



Fig. 82. — Orsat Apparatus. 



the most important of which are recording instruments giving 
the percentage of CO2 in boiler flue gas continuously. 

CO2 Recorders.* These may be divided into two classes, 
continuous and intermittent. Of the former, a representative 
one is the Uehling. Its principle is shown diagrammatically 
by Fig. 8S. A steam aspirator draws the gas through the two 
orifices, A and B, between which is a special, dry absorbent of 
CO2. If no CO2 is present, there will be a definite pressure, 
below atmosphere, between the two orifices. If CO2 is present 

* For methods of installing and adjusting various iy\)Qs of CO2 recorders, 
see Bulletin 91, Bureau of Mines, on Iftslrumcnts for Recording CO2 in Flue 
Gases, by Barkley and Flagg. 



40 



PRODUCTS OF COMBUSTION 



191 



it is absorbed between the orifices, reducing the volume of gas in 
this space, and thereby decreasing its pressure. Pressure there- 
fore becomes a measure of CO2 removed, and is recorded by a 
low pressure recording gage calibrated in percentages of CO2. 



TO BOILER ROOM INOJCATQR 



TO RECOROINC CAUCE 




ABSORPTION CHAMBER 

A 



INDICATING 
COLUMN-*- 



FILTER 



WATE R ^ ■ ■ ■ 6AS INLCr 

Fig. 83. — Diagram of Uehling CO2 Analyzer. 



The instrument is provided with a regulator for automatically 
maintaining a uniform flow. 

The Simmance-Abady CO2 recorder is typical of inter- 
mittent instruments for this purpose. Referring to Fig. 84, 
the water-sealed meter tank on the left alternately draws in and 
discharges a definite volume of flue gas by means of the rising 
and falling meter bell. This gas is delivered to the absorption 
tank, shown at the bottom of the figure, from which it is forced 



192 



PRODUCTS OF COMBUSTION 



40 



by the downward stroke of the meter bell into the recorder tank 
on the right, raising the counterbalanced recorder bell to a 
height proportional to the final volume of the gas. The last posi- 




<y Absorption Tank 

Fig. 84. — Diagram of Simmance-Abady CO2 Recorder. 

tion of the recorder bell is therefore a measure of the CO2 absorbed 
from the sample, and this measure is translated by the recorder 
pen. 

The motive power of the instrument is derived from water. 
A water aspirator, at the top of the machine (Fig. 84) main- 



40 PRODUCTS OF COMBUSTION 193 

tains a continuous stream of flue gas through the samphng pipe. 
The aspirator water then descends into the middle, or syphon 
tank, and raises a float. This float is connected with the meter 
bell which falls as the float rises. When the syphon tank is 
full, its water is quickly syphoned out: the float descends, and 
the meter bell rises and draws a charge of gas. The water 
falls into a pot below the syphon, thereby closing the control 
valve in the gas inlet pipe. The water is then emitted from this 
pot and allows the valve to open again. The recorder pen is 
released by the same action, arid an unbalanced weight causes it 
to travel until checked by a stop w^hich bears on the recorder 
bell in its final position. 

Reagents for Orsat Apparatus. For CO2, a 1 to 2, by weight, 
solution of potassium hydroxide (KOH) in water. Enough for 
charging one pipette, about 150 cc, may be made by dissolving 
60 gms. of KOH with 120 gms. of water. The reagent will absorb 
40 times its own volume of CO2. 

For O2, the reagent is a mixture of water, potassium hydroxide, 
and pyrogallic acid in the proportions of 20 to 21 to 1 by w^eight. 
The potassium hydroxide should first be dissolved in the water 
and then the pyro, in pow^der form, added. Enough for one 
pipette charge may be made by using 83 gms. of w^ater to 100 
of KOH to 4.25 pyro. The absorptive capacity is twice its own 
volume. 

For CO, the reagent is a 3 to 40 solution of cuprous chloride 
(CuCl) in w^ater. To this should be added just enough strong 
ammonia to cause a barely perceptible odor. Enough for one 
pipette charge may be made by using 11 gms. of cuprous chloride 
to 147 gms. of w^ater. The absorptive capacity is four times 
its ow^n volume. 

Sampling, F'or use in the apparatus, a small amount of the 
total gas is led from the main body through a sampling tube. 
The proper construction of this tube depends upon w^hether 
the gas is flowing in a large flue, as in boiler work, or in a com- 



194 PRODUCTS OF C0:MBUSTI0N 40 

paratively small pipe, as in gas engine work. For the latter 
it is sufficient to tap into the exhaust pipe a pipe of about J-inch 
diameter. In a boiler flue, however, the composition of the gas 
may vary through any section of the current, so means should 
be provided for dra^\ing gas f^om various parts of the section. 
One method of doing this is to run the sampling pipe diagonally 
across the flue, the end of the pipe being sealed and holes being 
drilled across the length in the flue. The holes should increase 
uniformly in size from the point of entrance of the sampling 
pipe to its end, as otherwise more gas will be drawn from the 
holes in the near end of the pipe. The pipe should enter as nearly 
as possible to the furnace, but beA^ond the combustion chamber 
or last pass in which combustion is taking place. This should 
be done because the farther the gas gets from the furnace the 
greater is its opportunity to become diluted with air entering 
through leaks in the brick work or setting. 

The sample may be collected with an apparatus sucn as shown 
by Fig. 81, consisting of two 3- and 5-gallon flasks connected as 
shown. The flask >S is used to receive the sample. To start with, 
it is filled with water. During collection, the water is syphoned 
into flask R through T' and the gas flows through H into the 
space evacuated, branch F being closed. 

All the air in the tube H should be displaced before taking the 
sample. This may be done either by raising the flask R above 
the level of the sampling tube so that water will syphon into the 
the tube //, or by drawing a small charge of gas into flask *S in 
the regular manner and then discharging it through a three- 
way cock at the end of the branch F. The latter procedure leaves 
flue gas in the tube H very slightly diluted with air. 

The sample should be collected at a uniform rate, and, if more 
than one sample of the same gas or for the same test is to be analyzed, 
time periods during which collections are made should be equal 
in order to get a correct average result. The rate may be kept 
practically uniform by placing flask R several feet below S and 



40 PRODUCTS OF COMBUSTION 195 

by choking the end of the syphon at t with a sHver of wood. The 
change in the rate due to the decreasing distance between the 
water levels in the flasks may then be inconsiderable. 

For boiler and gas engine tests, it is well to collect the sample 
during half hour or hour periods, and during the collection of 
each sample to analyze the preceding one. This has the advan- 
tage of showing the uniformity of combustion as the test proceeds. 
It is also well to have a duplicate sampling outfit, collecting gas 
at a very slow rate so that the sample will cover the whole test. 
This may be analyzed at the convenience of the experimeter; 
the results should check the average of the separate analyses. 

(a) Determination of CO2, O9, CO and N2. The Orsat 
apparatus is first connected with a rubber tube to the branch 
F leading from the sample bottle (see Figs. 81 and 82). The 
reagents in the pipettes are brought to the levels a, by manipu- 
lation of the bottle B, the three-way cock / being closed. This 
being done, and the cocks, d, 0, and m, closed, the water level 
in the burette is raised to the point n, thus expelling the air 
previously contained through the three-way cock / which is open 
to the atmosphere for that purpose. The pinch-cock C on the 
samjjling bottle flue connection is now closed, and the flask R 
raised so as to put the sample under pressure. The cocks 
between the sample bottle and the burette are then opened, 
and the bottle B lowered so that part of the sample will flow 
into the burette. The gas now in the burette is diluted 
with air or other gas which was in the distributing tube and 
in the rubber tube leading to the sampling bottle. To get a 
purer charge, this first one is discarded through the three-way 
cock, /, and another one brought into the burette, in the same 
way as the first, which may be accepted for analysis. This 
charge should be somewhat greater than 100 cc. 

Having secured this sample by closing the three-way cock, 
the bottle B is raised a trifle until the water level in the burette 
reaches the lowest graduation which marks 100 cc. of gas. As 



196 PRODUCTS OF COMBUSTION 40 

the sample has been compressed by this rise in water level, the 
pressure should be made equal to atmospheric by opening the 
three-way cock for an instant, the pinch-cock p being closed 
so as to maintain the water level at the lowest graduation. 

The sample should now be worked back and forth in the KOH 
solution to remove the CO2. After this has been done for a 
few minutes, it should be returned to the burette, care being 
taken that the reagent is at its original level, a; the cock d should 
be closed; and a volume measurement of the gas made. This 
must be done with the sample under the same condition of 
pressure as wlien originally measured, that is, atmospheric. For 
this reason, the w\ater levels in the burette and in the bottle B 
should be coincident when the reading is made. Before making 
the reading it is well to allow the walls of the burette to drain 
for a minute. After the reading the gas is returned to the KOH 
solution and worked a few more times, then measured again. 
If the volume is the same the result is satisfactory, if not, the 
process should be repeated until all the CO2 has been removed 
as indicated by constant volume. The diminution of volume 
is the per cent CO2. 

Tl e O2 and CO are removed and measured in the same Avay 
and in the order named. The difference between the sum of the 
per cents of CO2, O2, and CO, and 100 may be taken as the 
percentage of No. 

Precautions in Operating. Before using the apparatus, all 
connecting tubes and cocks should be tested for leaks by putting 
air in the system under pressure or partial vacuum with the 
bottle B, and noting whether the volume remains constant as 
shown by the level in the burette. 

Analyses should be made at a uniform temperature of not less 
than 60° F. During operation, the apparatus should not be 
exposed to a changing temperature, or placed where drafts or 
sun may strike it. The corresponding changes in the volume 
of the sample would give false results. 



40 PRODUCTS OF COMBUSTION 197 

Water absorbs all of the gases to some extent. To avoid 
the resulting errors, it is well to use water that has been previously 
saturated with exhaust gas, so that it will not take up any more. 
To do this the exhaust gas is caused to bubble through the water, 
used in the sampling flask and in the burette. 

If a little coloring matter, such as red ink, is added to the 
water used in the burette, it will aid in the reading of the gradua- 
tions. 

It is well to keep a record of the volumes absorbed by each 
reagent so that it will be known when their absorptive capacity has 
been reached. The volume of reagent in a pipette is about 150 cc. 

(b) Calculations from Exhaust Gas Analyses. The principles 
upon which these depend are stated and illustrated on pages 180 
to 183. They should be thoroughly understood. 

The results for coal combustion are generally based upon 1 
lb. of dry ccal, while those for fuel gas are based on one standard 
cubic foot of the fuel. Therefore two different sets of formulas 
will be deduced for the two cases. 

It is convenient to apply the following rule for a number of 
purposes. The density of a gas, in pounds per standard cubic 
foot, equals the density of hydrogen times the ratio of molecular 
weights of the gas and hydrogen. The density of hydrogen is 
0.00559 lb. per standard cubic foot; consequently the density 
cf gaseous carbon, for instance, is 0.00559 X 2' =0.0335. 

The following notation will be used for the two cases in com- 
mon 

D, ikf, 0, A", // = percentages cf carbon dioxide, monoxide, oxygen, 

nitrogen, and hydrogen, by volume, in the 
exhaust gas, respectively. 
Fd = volume cf dry exhaust gas in cubic feet per 

pound cf coal or per cubic foot of fuel gas. 
Tra = weight of air supplied in pounds per pound of 
coal, or per cubic foot of fuel gas. 



ja 



198 PRODUCTS OF COMBUSTION 40 

Tr4i = weight of dry exhaust gas in pounds per pound 
of coal, or per cubic foot of fuel gas. 

TT\ = weight of H2O in the exhaust gas, per pound 
of coal, or per cubic foot of fuel gas. 
X = excess coefficient; that is, the ratio of the 
amount of air supplied to that required for 
complete theoretical combustion. 

It should be borne in mind that the weights here tabulated 
are quantities resulting from the combustion of 1 lb. of dry coalj 
or from 1 standard cubic foot of fuel gas (see page 170). 

Formulas for Coal Combustion. In 100 molecule-feet of the 
exhaust gas there are D+M molecule-feet of carbon, since each 
per cent cf CO2 and CO contains 1 molecule-foot of carbon. 
Therefore, the ratio 100-^ (D+M) is the number of cubic feet 
of dry exhaust gas per cubic foot of gaseous carbon contained 
by it. This is for dry exhaust gas (that is, the volume cf the water 
actually contained is omitted) because the analysis does not 
take account of the H2O. If it is divided by the weight of a 
cubic foot of gaseous carbon, 0.0335 lb., the result is the number 
of cubic feet of dry exhaust gas per pound of carbon in it, or 
2980-f-(Z)+il/). Multiplying this by the weight of carbon 
that is gasified from 1 lb. cf dry coal, we have the volume cf dry 
exhaust gas per pound of dry coal, or 

Co 



rd-2980 



D+M' 



in w^hich Co is the weight of carbon gasified. This quantity is 
all of the carbon in 1 lb. of dry coal, G, except that lost through 
the grate and removed with the ash, C^; or 

Cg =^Ct — Ca 

assuming carbon deposited as soot to be negligible. Ct may be 
estimated from the proximate analysis and Ca measured from the 



40 PRODUCTS OF COMBUSTION 199 

total ash (Test 54 (c)). If Ct is found from the analysis in terms 
of percentage cf the coal as analyzed, that is, wet coal, it should 
be divided by 100 minus the percentage of moisture to reduce 
to weight per pound of dry coal. 

To find the weight of air supplied per pound of dry coal, 
we may assume that all of the nitrogen in the exhaust gas comes 
from the air, a very nearly correct assumption since coal con- 
tains but little nitrogen. Now, there are 28 N weights of N2 
in the exhaust gas, and 12{D+M) weights of C; 28 and 12 being 
the molecular weights, respectively. Therefore, the weight of 
N2 supplied by the air to each pound of carbon gasified is 

pounds. Dividing this by the proportion of N2 in 

air, 0.77 by weight, gives the pounds of air supplied to a pound 
of the carbon in the exhaust gas. Multiplying by the weight 
of carbon gasified from 1 lb. of dry coal gives the weight of air 
supplied per pound of dry coal, or 

Wa 



12X.77X{D+M) 

NCa 



3.04 



D+M 



The weight of dry exhaust gas is that of the air supplied 
plus that of the carbon combined with it, approximately-, or 

This is approximate since some of the oxygen in the air has 
combined with the H2 in the coal to form water which is sepa- 
rately counted. This, however, is comparatively small. Also 
other constituents than carbon from the coal are in the dry 
exhaust gas, oxygen and sulphur, for instance. With bituminous 



200 PRODUCTS OF COMBUSTION 40 

coals, the 0x3 gen may be as high as 10 per cent by weight, but 
this amount would figure as less than 1 per cent of the dry prod- 
ucts of combustion. 

Water vapor in the exhaust gas comes from three sources, 
namely from combustion of hydrogen, from moisture in the 
coal, and from the moisture in the air supplied. The first two 
only need be considered. 

If Ht is the weight of hydrogen in 1 lb. of dry coal, the result- 
ing water vapor, if all the hydrogen is burned, will be 9 //<, since 
the ratio of weights of H2O to the H2 in it is (2 + 16)4-2 = 9. 
If 771 is the weight of moisture in the coal per pound of dry coal, 
then the total weight of H2O in the exhaust gas, per pound of 
dry coal is 

The assumption that all the H2 is burned is sufficiently accurate 
under usual operating conditions. 

If lit and m are found from the proximate analysis (see 
Test 37, (a) and (6) ) as percentages of the coal as analyzed, 
they should be divided by 100 minus the percentage of moisture 
to reduce to pounds per pound of dry coal. 

The weight o'^ carbon incompletely burned, per pound of 
dry coal, may })e calculated from the CO appearing in the exhaust 
under the assumption that there is no incomplete combusti^^n 
through unl)urned hydrocarbons. The method is the same as 
for the determination of the weight of air. Let Wi be the 
desired weight. Then 



i 



12(£>+M) 



D+M 
To find the excess coefficient, it is necessary to divide the 



40 PRODUCTS OF COMBUSTION 201 

value of Waj as deduced above, by the expression for the air 
required as given on page 189, then, neglecting O2 in the coal, 

X = TT,,-^(11.6Cl+34.8//,). 

The formulas above also apply to the combustion of oils if 
Ct is substituted for C^, and if m is left out of the expression 
for Wv. 

Formulas for Gas Combustion. These are deduced upon 
the assumption that all the carbon in the fuel appears in the 
exhaust gas analysis, and that none other does. Contrary to 
this, in the case of internal combustion engines, is the fact that 
some carbon is left as a deposit in the cylinder, but it is so small 
compared with the total carbon used as to be negligible. Also, 
if the lubricating oil burns, it will appear as CO2 in the exhaust, 
so care should be taken to avoid this condition. Hydrocarbons 
in the exhaust, too, will prevent the correct application of the 
formulas. If the CO in the exhaust is less than 1 per cent, it 
is very unlikely that there is any hydrogen or hydrocarbon, 
because CO is the least readily burned of the fuel gas constituents. 

The following relation will be used to get most of the for- 
mulas. 

Weight or volume of the substance sought, per cubic foot 
of fuel gas = weight or volume of that substance contained in 
1 cu. ft. of exhaust gas X volume of exhaust gas per cubic foot 
of fuel gas. 

If an expression for the last named quantity, which is Fd, 
be deduced, it will remain only to find the required quantities 
per cubic foot of exhaust gas. 

The following additional notation will be used. 

Cjh^g =the number of molecule-feet in 100 molecule-feet 
of the fuel gas, of carl:on, hydrogen, and oxygen, 
respectively; counted as in columns 3, 4 and 5 of 
the table on page 294. 



202 PRODUCTS OF COMBUSTION 40 

R = Ratio, by volume, of air supplied to gas, that is, 
the numbr of cubic feet of air per cu. ft. fuel. 

To find Vd^ Since there are D+M molecule-feet of carbon 
in 100 of the exhaust gas, and c molecule-feet in 100 of the fuel 
gas. 

Cubic feet of exhaust gas per cubic foot of gaseous C in it 



Cubic feet of fuel gas per cubic foot of gaseous C in it = 



D+M 

100 



c 

By assumption, the gaseous carbon is the same in both gases. 
Hence, by division. 

Cubic feet of exhaust gas per cubic foot of fuel gas = 



T 



D+M 



The volumes of exhaust gas above are for dry gas. 

The volume of air supplied per cubic foot of fuel gas is found 
as follows. The oxj^gen appearing in 100 molecule-feet of the 
exhaust gas is D+0+.5M molecule-feet. Dividing this by 
.21, the proportion of oxygen in air by volume, gives the cor- 
responding amount of air; and the cubic feet of air which sup- 
plied this oxygen, per cubic foot of exhaust gas, is '- ■, 

^ -^^ ' 100X.21 

Multiplying by Vd^ gives the cubic feet of air per cubic foot of 
fuel, that came in with the oxygen that appears in the exhaust 
gas. But some oxygen has disappeared in the form of water. 
As there are h molecule-feet of hydrogen in 100 of the fuel, and 

as each one combines with half its volume of O2, is the 

2X100 

cubic feet of oxygen disappearing as water, per cubic foot of fuel. 
But some of the oxygen comes from the fuel itself, and we wish 
only that which comes from the air. Subtracting the molecule- 
feet of oxygen in the fuel gives {.5h — g)'^100. Dividing by 



40 PRODUCTS OF COMBUSTION 203 

0.21, we get the corresponding air. Then the cubic feet of air 
supplied per cubic foot of fuel gas is, 

If there is H per cent of hydrogen in the exhaust, too much 
oxygen has been counted. To allow for this, if the free hydrogen 
is known, subtract 0.5H from the quantity in the parenthesis. 

To find Wd' The density of CO2 in pounds per cubic foot is 

44 D 

0.00559 X-^ (see page 197). Multiplying this by -77^7 gives the 
z luu 

weight of the CO2 in one cubic foot of the exhaust gas. In the 

same way the weights of all the other constituents of the dry 

exhaust gas may be obtained, and there results 

'■^^^^{UD+32O+28M+28N)-^l00. 
Multiplying this by Fd, and simplifying, we have, 
Wa = ^{nD+80 + 7{M+N)}. 

To find Wv Besides the water of combustion, there is 
some water vapor in the exhaust due to moisture in the air and 
fuel gas. These will be disregarded, as they have but a sUght 
effect upon the heat analysis owing to the fact that latent heat 
is not lost to the H2O of humidity. 

Since there are rrrrj cu. ft. of hydrogen per cubic foot of fuel, 

and since the weight of the resulting H2O is 9 times the weight 
of the H2, we have, 

= . 0005/1. 



204 PRODUCTS OF COMBUSTION 40 

If hydrogen in the exhaust has been analyzed, 

W, = .0005(h-HVa) 

since free hydrogen would mean a corresponding decrease of H2O. 
The cubic feet of unburned CO per cubic foot of fuel equals 

Vi = MVa^ 100. 

If hydrogen has been found, it may be expressed similarly. 

To find the excess coefficient, the value of /?, as deduced 
above, should be divided by the expression for the air required 
as given on page 189, or 

217? 



X 



c+ .5h — g' 



Problem 40i. Draw a set of curves like Fig. 78 for the semi-anthracite 
coal whose ultimate analysis is C = 0.80, H = 0.04, = 0.03, Ash = 0.10. 

Problem 4O2. How many pounds of air are required to burn 1 lb. of the 
coal in the last problem? In this calculation, what per cent of error is involved 
if the oxygen contained in the coal is ignored? Ans., 10.5 lbs. 

Problem 4O3. How many cubic feet of air are required to burn 1 cu. ft. 
of the producer gas, analysis of which is given on page 165? What is the 
weight of this air? Ans.y 1.07 cu. ft. 

Problem 4O4. Figure the density of the producer gas of the last problem 
by the molecular weight method, page 197. A/is., .0703 lb. 

Problem 4O5. Deduce an expression for W^ similar to Wa, for coal. 

Problem 406. An exhaust gas analysis (coal) gives CO2, 6 percent; 
O2, 13 per cent; CO, 1 per cent; N2, 80 per cent. What are the weight and 
volume of total oxygen in it per pound of carbon gasified? Why would not 
a calculation for the air supplied, based on this result, give the same value 
as one based on the N2 in the exhaust gas? Ans., 7.43 lbs.; 83.1 cu. ft. 

Problem 4O7. An exhaust gas analysis from the illuminating gas in the 
table on page 165 gives CO2, 5 per cent; O2, 10 per cent; CO, 1 per cent; 
N2, 84 per cent. What are the values of R, Wa, W^j Ff, and X? 



PART THREE 

THE TESTING OF POWER PLANT UNITS 



41. The Determination of Cylinder Clearance 

Principles. Linear clearance of a piston engine may be 
defined as the least distance between the piston and cylinder 
head in a direction parallel to the center line of the cylinder, 
when the engine is on dead center. It may have different 
values at the head end and crank end of the stroke. 

Volumetric clearance is the cylinder volume between the 
piston and nearer cylinder end, which may be occupied by the 
working medium when the engine is on dead center. It may 
have different values on the two ends. The volumetric clear- 
ance is not only that in the bore of the cylinder, but includes 
the volume of the ports up to the valve face and the volume 
of any fittings, such as indicator piping, which may be filled with 
the working medium in the usual operation of the engine. The 
space in cylinder drain pipes open to the C34inder is sometimes 
considered as clearance volume; in some cases, however, this 
space, in usual operation, is filled with water of condensation 
so that it is not part of the clearance. 

Volumetric clearance is expressed as a part or per cent of 
the piston displacement. 

^^ Piston displacement '^ is the volume swept through by 

205 



206 STEAM ENGINE TESTING 41 

one stroke of the piston, that is, the area of the piston times 
the length of stroke. 

A knowledge of the clearance of engines is necessary to an 
analysis of their performance and losses, especially in connec- 
tion with indicator diagrams. See Tests 44 (a) and (6). 

(a) Linear and Volumetric Clearance by Linear Measurements. 
The most accurate way to determine linear clearance, if the 
engine is not too large, is to loosen the connecting rod when the 
piston is at the end of its stroke, and then note how far the 
piston rod moves when it is pushed from the dead center posi- 
tion to contact with the cylinder cover. If the engine is too 
large for this the cylinder cover may be removed, and the 
measurement made by compressing between it and the piston, 
a small quantity of putty. The putty should be stuck to the 
cover at the part where the distance between it and the piston, 
or the piston rod extension, appears to be least. The piston 
should first be oiled and then dusted with graphite, so that the 
putty will not stick to it. The putty is then compressed by 
bolting the cover in place. The least thickness of the putty 
is the linear clearance. It may be measured by the use of a 
piece of fine, stiff wire. 

The volumetric clearance may be obtained by mensuration 
from the drawings of the engine. This gives only an approximate 
result since the actual castings may differ materially from their 
drawings, and since the position of the piston in the cylinder 
may change with wear of the connecting rod bearings. If 
mensuration is used, it is best to make drawings of the engine 
clearances from the engine as it stands, as nearly as possible to 
scale. 

(b) Volimietric Clearance by Water Measurement. The 
engine should be put on the desired dead center by putting the 
crank and connecting rod in line by eye. The steam valve 
or valves should be made tight either by smearing its face with 
heavy cylinder oil or, with sHde valves, by squeezing a piece 



41 STEAM ENGINE TESTING 207 

of rubber gasket between the valve face and seat. The piston 
and cyUnder bore should be well oiled to prevent leakage. If 
the cylinder has holes tapped on the top for indicator piping, 
they may be used for the introduction of water by which the 
clearance volume may be completely filled. By taking the 
weight of the water before and after filling, the amount necessary 
to fill the clearance space is determined. Dividing this by the 
density of the water gives the clearance volume. The density 
may be taken as 0.0361 lb. per cubic inch at 60° F. If the tem- 
perature is materially different from this, it should be noted 
and the corresponding density used. 

Should there be a slight amount of leakage which cannot be 
prevented, it may be corrected for by determining the " leakage 
rate.'' This is done by measuring the amount of water necessary 
to keep the clearance space full for a period of one minute. 
Now, this is probably the maximum rate of leakage, since, dur- 
ing the filling, the leakage probably varied with the head of water 
in the cylinder. The average leakage may be taken as one- 
half that shown by the test. The period of time necessary 
for the filling should therefore be multiplied by one-half the 
maximum leakage rate to get the total leakage that occurred 
during filling. This weight subtracted from the weight used 
in the filling gives the weight corresponding to the actual 
clearance volume. 

It should be noted that there are several assumptions in the 
foregoing which make the method approximate; it should not 
be used when the leakage is very large. 

If the cylinder to be tested contains pockets in which air 
may be trapped during the fiUing, as is likely to be the case with 
internal combustion engines, these pockets should be blanked 
off and measured separately if possible. If this is not possible, 
the water method should not be used. 

For accurate results, several determinations should be made 
and none accepted unless they show fair agreement. 



208 STEAM ENGINE TESTING 41 

To express the clearance volume in percentage, the piston 
displacement must be known. The bore may be measured with 
inside calipers, and the stroke by measuring the distance between 
dead center positions of the cross-head, a mark being made on 
the cross-head guides at each end to indicate these positions. 

(c) Volumetric Clearance from the Indicator Diagram. Pro- 
fessor Paul Clayton proposed a method based on the fact that 
gases and vapors expanding or being compressed in closed 
cylinders follow the law that 

Absolute pressure X volume^ = a constant. 

This law is represented by a logarithmic curve. Consequently 
if the amounts of the pressures and volumes obeying it are plotted 
on logarithmic coordinating paper (the coordinates being pro- 
portional to the logarithms of their markings as with the scale 
of a slide-rule), the result is a straight line. In an indicator 
diagram, the volumes represented are the total volumes of the 
working medium behind the piston, which include that of the 
clearance space. In order to transfer the indicator diagram 
to logarithmic coordinates, then, it is necessary to know the 
clearance volume so that the axis of abscissas may be located. 
If the indicator diagram is located on logarithmic coordinates 
by assuming a value of the clearance volume, the resulting 
expansion and compression curves v;ill be concave to the origin, 
if the assumed value is too small, and convex if too large. This 
provides a method of determining the clearance volume, since 
it is only necessary to plot the expansion or compression curve 
from the indicator diagram on the logarithmic scale using a 
number of assumed values of tl:e clearance volume until that 
one is found which produces a straight line. A convenient 
procedure is as follows. 

Divide the indicator diagram with equidistant vertical lines into 
ten spaces, and mark the points of intersection of the verticals 



41 STEAM ENGINE TESTING 209 

with the expansion curve 1, 2, 3, etc. The coordinates of these 
points will be used to locate the logarithmic diagram. The 
absolute pressures corresponding to these points should be 
measured from the zero pressure line which is laid off 14.7 lbs. 
below tlje atmosphere line. After choosing a suitable scale 
with w^hich to represent these pressures on the logarithmic 
chart, their positions are indicated by placing small marks against 
the vertical axis of logarithmic coordinates. Now, let a value 
of the clearance volume, x, be assumed in per cent. Then 
the point, 1, corresponds to a volume of 10 j^lus x per cent; point 
2, to a volume of 20 plus x per cent, and so on. Using these 
volumes expressed as percentages, the points are readily located 
on the logarithmic chart. If the resulting curve is concave to 
the origin, a larger value of the clearance is assumed, and so on 
until that value w^hich produces a straight line is found. 

It will be noted that there are limiting values of the assumed 
clearance between w^hich the straight line condition seems to 
be satisfied. On this account the method is recommended 
only where the clearance is large, as in internal combustion 
engines; the percentage of error then being not excessive. 

Problem 41i. Following are the data from a test for volumetric clear- 
ance by the water method. Weight of bucket and water before filling, 
12 lbs. 141 ozs. Weight after filling, 10 lbs. 2h ozs. Time of fiUing, 
95 seconds. To keep clearance space full for 60 seconds, 8 ozs. What 
is the average leakage rate in pounds per m^inute? What is the clearance 
in cubic inches allowing for leakage? What is the per cent of clearance if 
the engine is 10 ins. X 16 ins. (bore X stroke)? Ans.y 5.22%. 

Problem 4l£. In the preceding problem room temperature 60° F. of the 
water is assumed. How much percentage of error w^ould be involved if 
the actual temperature were 40° F.? If 80°? Arts., 0.1%, 0.3%. 



210 



STEAM ENGINE TESTING 



42 



42. Valve Setting of a Simple Slide Valve Engine 



Principles. It is assumed that the student is acquainted 
with the principles and operation of the simple slide valve and 
linkage and ^^ith the various quantities pertaining, such as steam 
lap, exhaust lap, angular advance, etc., which subjects are amply 
covered by various works on the steam engine. 

With a finished steam engine, in order to set the slide valve 
so as to better the distribution of steam, there are only two parts 
that may be adjusted without altering the design of the parts, 
namely, the valve stem, which may be changed in length, and 
the eccentric, which may be changed in its position on the 
shaft relative to the crank. The former adjustment affects 
the laps and lead of the valve; the latter, the angular advance. 
A study of the valve motion will show the effects of such adjust- 
ments upon the valve and upon the steam distribution as follows. 





Effect of Increasing. 




Angular Advance. 


Stem Length. 


On 


Head End. 


Crank End. 


Head End. 


Crank End. 


Outside lap 

Inside lap 


Same 

Same 

Increases 

Earlier 
Earlier 
Earlier 
Earlier 


Same 

Same 

Increases 

Earlier 
Earlier 
Earlier 
Earlier 


Increases 
Decreases 
Decreases 

Later 
Earlier 
Earlier 

Later 


Decreases 
Increases 


Lead 


Increases 


Admission 


Earlier 


Cut-off 


Later 


Release 


Later 


Compression 


Earlier 



The student should confirm this table by drawing the link- 
age as in Fig. 85 to represent the positions at the various events 
of the stroke, taking them first for one end of the cylinder and 
then the other, and observing from the drawings the effects of 



42 STEAM ENGINE TESTING 211 

the adjustments as tabulated. In Fig. 85 the engine is shown 
at crank end release. The valve stem is broken so as to show 
the valve on top of the cylinder, for convenience, instead of. 
at the side. 

It should be noted that the laps may be measured when the 
eccentric is vertical, as this position of the eccentric puts the 
valve practically in its mid-position. 

(a) Measurement of Lead. This is made by measuring the 
amount of port opening, the valve chest cover being removed, 
when the engine is on dead center, that is, w^hen the crank and 
connecting rod are in line. The engine should not be put on 
dead center by noting the extreme position of the cross-head 



'¥^ 



YdlveSfeyn 



Eccenrric-') 




f/y//A////A 
Fig. 85. Fig. 86. 

because, at the end of the stroke, there is no appreciable move- 
ment of the cross-head when the crank moves through several 
degrees. The eccentric, however, is then in a position where a 
few degrees of error will cause a considerable error in the position 
of the valve. Consequently, the dead center must be accurately 
located. The following method may be used. (See Fig. 86.) 
The crank is turned until it is about 30 degrees from the 
dead center position sought. A mark, 1, is then made on the 
cross-head against a mark, 2, on the guides. Another mark, 
3, is made on the flywheel against a mark, 4, on some stationary 
object. Now the engine is turned through its dead center posi- 
tion until the cross-head mark 1 again comes into the coincidence 
with 2. The crank and connecting rod will then occupy the 
positions shown by the dotted lines and the mark 3 a\ ill be at 



212 STEAM ENGINE TESTING 42 

5. A new mark is now made on the flywheel opposite 4, and 
the distance between this and 5 on the flywheel rim is bisected 
by the line 6. If the flywheel is then turned until 6 is opposite 
4, the engine will be on dead center. Care should be taken 
that the motion of the linkage, when advancing to the positions 
for marking, should always be in the direction of the dead center 
sought so as to avoid error through lost motion of the parts. 
If there is no place conveniently near on which to put the mark 
4, a pair of trammels should be used. 

(b) Setting the Valve for Equal Leads. From the table 
given under '^ principles/' it is seen a change in the angular 
advance will make the leads on both ends larger or both smaller, 
while a change of the stem length will make the lead on one 
end larger and on the other smaller. It will therefore be con- 
venient to change the stem length to equalize the leads, and then 
to adjust the angular advance until they become the desired 
amount. The procedure is as follows. 

The eccentric is first put in its approximate position, that 
is, about 135° ahead of the crank. The leads are then meas- 
ured according to (a). If the lead on the head end is greater 
than on the crank end, the stem length must be increased to 
equalize them, and vice versa (see table). If the leads are 
then both too small, the eccentric is shifted on the shaft further 
away from the crank until the desired leads are obtained, and 
vice versa if the leads are too large. 

The proper amount of lead depends upon the travel of the 
valve, the engine speed, and the amount of compression. More 
lead is required for high speed engines, and less when the com- 
pression is high. For low speed engines, leads up to re ^^- ^re 
usual, and for high speeds, twice that amount. 

It is advisable, after setting for equal leads, to indicate the 
engine as a check upon the setting. The lead should be such 
as to give a vertical line at the admission for both head and 
crank ends. 



42 



STEAM ENGINE TESTING 



213 



(c) Setting for Equal Cut-offs by the Bilgram Diagram. 
The typical Bilgram diagram is shown by Fig. 87, the positions 
of the crank corresponding to the various events of the stroke 
being shown (for the head end only) by the radial lines. The 
events of the stroke for the crank end may be found by reference 
to the crank end lap circles with similar construction. For 
convenience the lower half of the diagram may be revolved 
through 180° so as to be superposed on the upper half. For 
other details and for proof, see Halsey's Valve Gears. 



Rad = Head End St Lap- 
" f>/7. " •• 



Cranff Posifion fbr Admission - 0/ 

» » » Cuf-O-ff - 0? 

'• •♦ Release - OZ 

" • »' Compression ■ 04 



L Cross head J Conn. Rod. -^ 



6^roke 



Bad. • Crank End St Lap- 
" • •• >' E^h. ••- 




Rad. 'Eccen. 



Fig. 87. — Bilgram Valve Diagram. 



To lay out the diagram for the purpose of valve setting, 
we must assume a cut-off, and measure the connecting rod and 
crank lengths and eccentricity from the engine. If the cut-off 
is C inches from the end of the stroke, the corresponding crank 
positions, 01 and 02, may be found by drawing the engine link- 
age to scale as in Fig. 88. The diagram may be constructed on 
these lines, starting by putting in the eccentric circle as shown. 

The values of the steam laps will depend upon the setting 
of the valve, but we may locate the lap circles by determining 
the sum of the steam laps. This equals the length of the valve 



214 



STEAM ENGINE TESTING 



42 



in the direction of its motion minus the distance between the 
outside edges of the ports, in the case of the D-valve taking steam 
outside. The steam lap circles may be constructed by first 
locating a point x on the eccentric circle such that the sum of 
its perpendicular distances from the lines 01 and 02 equals the 
sum of the steam laps. The lap circles may now be drawn 
about x as a center and tangent to the lines 01 and 02. The 
leads and maximum port openings are then determined as shown. 
If the leads are too large, a later cut-off must be assumed and 
the construction repeated. 



C. E. St Lai 




Bad ' Conn. Rod Lencjih 






Fig. 88.— Setting for Equal Cut-offs. 



Using the data for the lead and port opening at one end 
(preferably the crank end, since there they are larger) the valve 
may now be set for the assumed cut-offs. To do this, the crank 
is revolved until the valve has moved as far as it will toward 
the head end of the cyUnder, thus giving the maximum port 
opening on the crank end and making the eccentricity parallel 
to the engine center line. The stem length is then adjusted 
until the crank end port is open an amount equal to that indicated 
by the diagram. Next the engine is put on its crank end dead 
center by the method given under {a) and the lead made equal 
to that shown by the diagram by s\\inging the eccentric on the 
shaft. This completes the setting, but the lead and port opening 



42 



STEAM ENGINE TESTING 



215 



should be measured on the head end as a check, and conipared 
with the values given by the diagram. 

(d) Valve Setting by the Indicator. The ultimate test by^ 
which the steam distribution must be judged is by the indicator. 
The valve setting should be such that not only does the engine 
run smoothly, but that it should give the maximum power for 
the steam used. 

Valves may be set by deductions from the indicator diagrams, 
and the previously described methods dispensed with. The 
procedure may l)e more laborious and less systematic, since it 
is largely cut and try. 




Events +00 Ewrli^ Even+s foo Late 

Fig. 89. — Faulty Valve Setting shown by Indicator Diagrams. 



Fig. 89 shows indicator diagrams, superposed on ideal ones 
represented by dotted lines, from Vfhich may be noted the 
variations caused by too early and too late occurrence of the 
events of the stroke. 

If the admission is too early (that is, if there is too much 
lead), full boiler pressure is admitted to the cylinder before the 
beginning of the stroke and the admission line rises at a point 
other than the extreme of the diagram. If the admission is too 
late (too little lead), the admission line slants inward because 
the full boiler pressure does not reach the cylinder until the piston 
has advanced appreciably in its forward stroke. 



216 STEAM ENGINE TESTING 42 

The cut-off may be too early on either end of the cylinder 
only in relation to that on the other end; they should be approx- 
imately equal for equal division of the load. The simple slide 
valve engine does not cut off earlier than six-tenths of the stroke; 
if the cut-off on either end is much later than this, as shown by 
the point at which the expansion line begins on the diagram, 
either the valve is not well designed or its setting is imperfect. 

If release takes place too earty, the pressure is released from 
the cylinder before the end of the stroke; the result is a curtail- 
ing of the expansion line and a sharp drop down to the backpres- 
sure line. If the release is too late, expansion may take place 
clear to the end of the stroke, but when the piston returns there is 
not enough opening for the steam to exhaust through freely. 
The result is excessive back pressure at the beginning of the 
return stroke as shown by the rounded toe of the diagram in 
Fig. 89. 

The compressions on the two ends should begin at approx- 
imately the same percentage of the stroke. If there is too little 
compression, the engine will not run smoothly; if too much, the 
maximum power is reduced, although the economy in the use 
of steam may be increased. Compression tends to reduce the 
steam loss due to clearance. 

To set a slide valve by the indicator, it is necessary to have 
diagrams from both ends of the cylinder. Faulty steam dis- 
tribution may then be deter- 
mined in detail by the effects 
on the diagrams as just de- 




scribed. A knowledge of the 
effects of the adjustments of 
stem length and eccentric 
Fig. 90. position, as given in the table 

on page 210, then enables 
one to correct the steam distribution. The engine should then 
be indicated again, and further corrections made if necessary. 



42 



STEAM ENGINE TESTING 



217 



As an example of the reasoning involved, consider Fig. 90. It 
is well first to make a table showing the existing characteristics 
of the diagrams, as follows: 



Admission. 

Head end Early 

Crank end Late 



Cut-off. 


Release. 


Compression. 


Late 


Late 


Early 


Early 


Early 


Late 



By reference to the table on page 210, it is seen that to change 
the angular advance will aggravate some of the errors, which- 



Ecoentrio 
too far ahead. 




Fig. 91. — Faulty Valve Setting and Diagrams. 

(Reproduced from Power.) 

ever way it is adjusted. But if the stem length is increased, 
the events will tend to equalize and change to proper amounts. 
The stem length should therefore be increased and diagrams 
taken, the procedure being repeated until the cut-offs are about 
equal. It may then develop that all of the events are too 



^^ 



218 STEAM ENGINE TESTING 42 

early or too late, in which case the eccentric should be adjusted 
until the admission lines are vertical. If the release and com- 
pression are then satisfactory, the setting is acceptable. Samples 
of indicator diagrams showing faulty valve setting, etc., are 
shown by Fig. 91. 

(e) Study of the Steam Distribution by the Bilgram or Zeuner 
Diagrams. This may be done before or after setting the valve 
in order to decide upon the best setting or how the setting may 
be improved, thus possibly saving a number of trial settings and 
of indicator trials. For this purpose, the necessary measurements 
are made of the valve and engine parts, from which a number of 
diagrams are constructed with different adjustments of eccentric 
and stem length assumed. Indicator diagrams may be con- 
structed from the data yielded by the Bilgram or Zeuner diagrams 
(the expansion and compression curves being drawn as rect- 
angular hyperbolas), by comparison of which, the best setting 
may be selected. 

The measurements to be made from the engine are of the con- 
necting rod and crank lengths, the eccentricity, and the lead and 
outside and inside lap on one end. The outside lap at either 
end may be readily determined by noting the distance th^ valve 
must move from mid-position to begin to uncover the port. 
The mid-position may be found by making a prick point or 
scratch on the valve stem and measuring to this mark. The 
inside lap at either end may be obtained by subtracting 
from the length of the valve face, the length of the port and the 
outside lap, the dimensions being taken from the end considered. 
The sum of the outside laps should also be found as described 
under (c), and the sum of the inside laps, found similarly, by 
subtracting the distance between the inside edges of the valve 
faces from the distance between the inside edges of the ports. 

The Bilgram diagram may now be laid out by drawing first 
the eccentric circle and the lead at the end for which it has been 
measured, say the head. (See Fig. 87.) Next, the head end 



42 



STEAM ENGINE TESTING 



219 



lap circle is drawn with its center at such a point, x, on the eccen- 
tric circle as to make the lap circle tangent to the lead line. The 
angular advance line is then drawn in, which locates the centers 
of the other lap circles. 
Having described these the 
events of the stroke, in per- 
centages, may be deter- 
mined. 

The Zeuner diagram may 
be laid out similarly, start- 
ing with the eccentric circle 
(see Fig. 92). A point X 
is then located at a dis- 
tance from the center of 
the eccentric circle equal 
to the lap plus the lead on 
the head end. The circle 
OX A is next constructed, 
which fixes the angular advance by the line OA. When the 
lap circles are put in, the events of the stroke may be determined 
in the usual manner. 

It may be noted that it is convenient to work with the sum 
of the outside laps and of the inside laps, since, if it is desired 
to reconstruct the diagram with a different lap on one end, the 
opposite one is readily determined by subtraction. 

Verify the table on page 210 by the method given in the 




Eccen. 



Fig. 92. — Zeuner Valve Diagram. 



Problem 42i. 

text following it. 

Problem 422. The lead on the head end of a steam engine is found to 
be TS in., and on the crank end A in. If the leads are to be made equal to 
ihb in., should the valve stem be lengthened or shortened and how much? 
Should the angular advance be increased or decreased? 

Problem 423. A D-slide valve has a face 1.5 ins. long at each end, and 
the distance between the faces is 2.75 ins. The ports are each H in., and 
the outside edges of the ports are 4.50 ins. apart. If the head end outside 
lap is .625 in., what are the values of the other three laps? 

Ans., f, 



3 
16) 



A in. 



220 STEAM ENGINE TESTING 43 

Problem 424. The valve in the preceding problem has an eccentricity 
of 1.375 ins. Find the lead and the maximum port opening on the crank 
end for equal cut-offs, using the Bilgram diagram. The connecting rod is 28 
ins. long and the crank 5 ins. 

Problem 42> Find the events of the stroke in per cents, using the data 
of the last problem and the Bilgram diagram. 

Problem 426. Repeat the last problem, using the Zeuner diagram. 

Problem 42;. Why cannot a valve be set for equal leads and equal cut- 
offs at the same time? If for equal leads, which cut-off is greater? 

Problem 428. How could the events of the stroke be measured direct 
from an engine whose valve was set, by reference to the valve and measure- 
ments of the cross-head travel? 

Problem 429. Set the valve of an engine for equal cut-offs. Then measure 
the events of the stroke from the engine, from the indicator diagram actually 
obtained, and from the Bilgram diagram. 



Test 43. Setting a Corliss Valve Gear 

Principles. The action of the CorHss valve gear is explained 
in numerous works on the steam engine. The student should have 
an understanding of this action to grasp the following: 

The setting may be considered in two parts; first, for the 
proper laps and leads, and, second, for the governor regulation. 
Usual values of the laps and leads are as follows, the smaller 
ones corresponding to the smaller engine sizes. 

Steam lap ^ to ^ inch. 

Exhaust lap . . i^ to 3^ inch. 

Lead A to | inch. 

The laps are adjusted and measured when the linkage is in 
its mid-position, as indicated by Fig. 93. This figure also names 
the terms by which the various parts will be referred to, so that 
the following instructions may be understood. 

(a) Adjustment of Laps and Leads. The first step is to set 
the wrist plate in its center position, the hook rod being lifted 
to free the wrist plate. There is generally a mark on the wrist 
plate hub which registers with three stationary marks, as shown in 



43 



STEAM ENGINE TESTING 



221 



Fig. 93. The middle stationary mark indicates the correct center 
position of the wrist plate, and the outer marks, its extreme 
positions. If desired, the center position may be checked with 
a plumb line. Having located this, the hook rod length should 
be adjusted so that, when engaged with the wrist plate, the rocker 
arm stands vertical as shown by a plumb hne. The eccentric 




Fig. 93. 



rod length may now be adjusted so that the eccentric throws the 
wrist plate to the correct extreme positions. 

Now, with the wrist plate in its center position and the steam 
valves hooked up, the laps may be made the desired amounts 
by altering the lengths of the steam and exhaust links. The 
laps are readily measured when the exhaust bonnets are removed, 
as lines will be found to indicate the edges of the valves and 
ports. This accomplished, put the engine on head end dead center 
(see Test 42 (a) for method) and make the head end lead the 
selected value by swinging the eccentric on the shaft, thus moving 
the valve to the desired position for lead. Then fasten the 



222 STEAM EXGIXE TESTING 43 

eccentric, put the engine on the other dead center, and measure 
the crank end lead. If the leads are not equal, the crank end 
steam link may be changed in length slighth' to obtain equahty. 

(b) Adjustment of Governor Rods. With the governor in 
the lowest running plane (but not in the safety stop plane), throw 
the wrist plate b\' hand to the head end limit as shown by the 
mark on the wrist-plate hub. The crank-end knock-off cam should 
then trip its valve just at this extreme wrist plate position; if 
it does not the crank end governor rod length must be changed. 
This done, the head end rod is dealt with similarly. The cut-oflfs 
will then be latest when the governor is in its lowest running 
plane. 

The no-load action of the governor should next be checked. 
Block up the governor to its highest plane, in which position 
the steam valves should just fail to hook up. 

Another procedure is to set the governor rods at the highest 
position of the governor so as to open the valves a very small 
amount when the valves are tripped; and, for the lowest position 
the valves are not released at all. It is understood that a setting 
at one limit of the governor travel cannot be made without 
affecting that at the other. 

(c) Adjustment of Dash-pot Rod. Each steam valve hook 
engages with a '' catch-block " on an arm rigidly fastened to the 
valve, and this arm is connected with the dash-pot rod. By 
lengthening or shortening the dash-pot rod, the catch-block may be 
raised or lowered. When the valve hook is in its lowest position 
(that is, when the wrist plate is at an extreme position), the cor- 
responding dash-pot rod should be changed in length until there 
is an equal clearance above and below the catch-block, between 
it and the hook. 

(d) A Check of the Setting by Indicator should be made after 
the completion of all adjustments. In particular, the amount of 
compression should be ascertained, and the action of the dash-pots 
towards a sharp cut-off, together with the equahzation of cut- 



44 • STEAM ENGINE TESTING 223 

offs. Improvements in the setting may be made often by changing 
the steam and exhaust Hnks. 

Problem 43i. Will increasing the length of a steam link increase or 
decrease the lap and the lead? Why? What effect will an increase of the' 
angular advance have on laps and leads? Why? 

Problem 432. If an indicator diagram shows the compression on the head 
end to be too early, should the exhaust hnk length be increased or decreased, 
and what effect will the readjustment have on the release? 



44. The Mechanical Efficiency Test of a Steam Engine 

Principles. The mechanical efficiency of a steam engine is 
equal to the useful horse-power divided by the horse-power 
developed by the steam in the cylinder. If a Prony brake is 
used to measure the useful horse-power, then (see Test 6) 

B.h.p. = BTFiV 

is the useful horse-power. 

Using the following notation, 
I.h.p. = Indicated horse-power; 
Pji and Pc = the mean effective pressure on the head end and 
crank end respectively; 
L = the length of the stroke in feet; 
a = the area of the cylinder, in square inches; 
a' = the area of piston rod, in square inches; 
iV = the number of revolutions per minute; 
then the cylinder horse-powder may be expressed, 

On the head end, I.h.p.^ = ^ =KnPhN, . . (1) 
On the crank end, I.h.p.c = ^'^J^ I.^'- ^ = KcPcN (2) 

oo, UUU 

Kj, and Kc are called the " engine constants." 
Total I.h.p. = I.h.p.ft4-I.h.p.c. 



224 STEA:\I EXGIXE testing 44 

^Mechanical friction causes a loss of power so that all the 
work developed in the cylinder does not appear at the fl^-wheel. 
The friction horse-power equals 

F.h.p. = I.h.p.-B.h.p (3) 

When the brake is entirely removed from the engine, the work 
done in the cylinder to keep the engine running is expended to 
overcome friction only. 

The function of the engine governor is to keep the speed 
constant. This is done by the action of any change of speed, 
through centrifugal force, to alter the position of the governor 
weight. More or less steam is admitted into the cylinder accord- 
ing to the position of this weight, and therefore more or less 
cylinder work is done. To accommodate itself to a variable 
load, then, the engine 7?iust allow some change of speed to 
regulate the cylinder work. At no load, with the governor 
admitting the least steam, the speed is greatest, and at maximum 
load, least. Good regulation requires that the difference between 
these limits of speed be small. 

For comparative purposes the speed regulation is expressed 
as a percentage variation from the mean speed. If Xm and Nn 
are the speeds at maximum and no load, respectively, then 

Per cent speed regulation =^ .^.^^^ ^^.*". ' ^T xiOO. 

(a) The Indicated Horse-power is determined by measur- 
ing the quantities in formulas 1 and 2, the engine constants 
being calculated before the test. The mean effective pressures 
are found from indicator diagrams by integration with a plan- 
imeter. The speed is determined with a Ijand or continuous 
counter. 

The brake horse-power being the independent variable, it 
is first calculated what net forces should be obtained at the 
brake scales to produce the required horse-powers. The engine 



44 STEAM ENGINE TESTING 225 

is then operated at one of these horse-powers by adjusting the 
tension of the brake strap to give the necessary force at the 
scales, and to maintain it at that value. This means constant 
observation of the brake scales and occasional regulation of the 
brake-strap tension. The engine should be operated at each 
load for ten minutes or more so that it may adjust itself to the 
new conditions of load and friction. A number of indicator 
diagrams and measurements of the R.p.m. are then taken. It 
is convenient to average the readings of Pn, Pc, and N at each 
load and to use the averages for substitution in formulas 1 and 2. 
A more convenient, although approximate, formula for 
calculating the indicated horse-power, is as follows: 

Ui.p. = k{Pb+Pe)N 

in which k is the average of the two engine constants or L( a— — J 

-T- 33,000. A brief consideration will show that the more nearly 
is the area on the crank end equal to that on the head (that is, 
the smaller is the area of the piston rod relative to that of the 
cylinder) the less error is there in the approximate formula. 
Also, the less difference is there betv/een the mean effective 
pressures on the two sides of the piston, the less error is there. 
When they are equal the results from the two methods of calcu- 
lation are the same. 

The following is a rational formula by which the per cent of 
error ensuing from the approximate formula may be determined 
for any conditions. Let 

iR = Ratioof P^toPft; 
<i = Diameter of the piston rod, inches; 
Z) = Diameter of the cylinder bore, inches. 
Then 

Per cent of error = 50 X 7^ X :r-rT,' 



226 STEAM ENGINE TESTING 44 

Using this formula, it will l^e found with usual proportions 
of d and Z), that the mean effective pressure on one end must be 
two or three times that on the other to produce more than one 
per cent of error. It is thus clear that the a])proximate calcu- 
lation may almost always be used, since any engine with prop- 
erl}^ set valve would give a more uniform division of the load 
than this under normal conditions. Some engines divide the 
cylinder work quite unequally at light loads; in such a case 
the formula will show whether or not the correct method should 
be used. A convenient rule is as follows: 

If the mean effective pressure on one end is not greater than 

bQd?-D^' 

times the mean effective pressure on the other y then the error is less 
than 1 per cent. 

(b) The Friction Horse-power at each load is found as 
indicated by formula 3. Tests have shown that this quantity 
is very nearly constant at all loads of a given engine, if properly 
operated. As the conditions of lubrication affect friction and 
therefore mechanical efficiency, the lubrication should be given 
special attention and maintained uniform throughout the test. 
It is advisable to plot a curve of F.h.p. -vs. B.h.p. as the test 
progresses as this is closely indicative of the accuracy of the 
results. 

(c) The Efficiency is found by dividing each value of the 
B.h.p. by the corresponding value of the I.h.p. 

(d) Speed Regulation. Values of Nm and Nn have been 
obtained for the other results, and these may be used to get 
the speed regulation. Another test consists in quickly throwing 
the entire load on or off and noting the resulting momentary 
variation in speed. This is greater than that produced by a 
gradual change of the load, and it should be deteniiined with a 
chronograph or tachagraph. 



44 STEAM ENGINE TESTING 227 

Any change in boiler pressure will affect the speed regulation, 
so this should be kept constant during the test if possible, and 
any variations noted. 

Problem 44i. If the F.h.p. is constant at all values of the B.h.p., deduce 
the forms of the curves of B.h.p. vs. I.h.p. and efficiency vs. B.h.p. Will 
these curves pass through the origin or not? Why? 

Problem 442. Figure what may be the maximum ratio of mean effective 
pressures with a 14-in. X30-in. engine having a 2i^-inch piston rod, so that 
the error from using the approximate formula for I.h.p. will be less than 1 
per cent. Ans.y 5, nearly. 

Problem 443. Calculate the length of the adjustable arm of a polar 
planimeter, so that horse-power may be read direct when indicating the engine 
in the preceding problem. (See Test 14 (d).) The diameter of the record 
wheel is 0.79 in. and there are 100 graduations on the wheel. One graduation 
to equal 1 H.p. Length of indicator diagram = 5 in. Spring scale = 60. 
Average value of A^ is 80. Ans.j 3.62 in. 

Problem 444. A 50-horse-power engine running at 200 R.p.m. is tested 
with a brake with an 8-ft. arm. If its unbalanced weight is 10 lbs. and the 
weight of the pedestal by which its thrust is transmitted to a platform scales 
is 5 lbs., what should be the scale readings for an efficiency test of six runs? 

Ans.y 179 lbs., max. 

Problem 445. Run a series of tests on a steam engine to show the rela- 
tion between steam pressure at admission if the governor is throttling, or 
cut-offs, if of the cut-off type, under variable brake horse-power. 



45. Economy Test of a Steam Engine 

Principles. Economy tests on steam engines are made to 
determine the amount of steam and heat they consume per unit 
of power, under different conditions. The most important 
variable in such tests is the brake horse-power; it is usual to 
vary it throughout the working range for a complete economy 
test. « 

Economy results should always be based on the brake 
horse-power, but the indicated horse-power is often used because 
it is inconvenient or impossible to brake the engine. The unit 
^^ horse-power-hour '^ will be used, meaning the amount of work 
developed in one hour b^^ one horse-power. The heat equivalent 



228 STEAM ENGINE TESTING 45 

of this work should be remembered. Since 33,000 foot-pounds 
of work are developed in one minute by one horse-power and 
778 foot-pounds equal one B.t.u., then in one hour 

^^^X60 = 2545 B.t.u. = l H.p.-hr. 

The steam supplied to the engine is generally expressed in 
pounds per horse-power-hour, that is, the pounds of steam sup- 
plied in one hour divided by the horse-power. The result should 
be considered in connection with the condition of the steam, 
since less will be needed at high pressure or superheat, and 
more if it is wet. One practice is to quote the steam consump- 
tion in pounds of ^^ equivalent dry steam, ^' that is, the pounds 
of dry steam that contain the same number of heat units as 
the total H2O actually supplied. Since these amounts of steam 
have not by any means equivalent capacities for doing work, 
and since the costs of making wet, saturated, and superheated 
steam of the same heat content are not the same, this seems 
hardly worth while. It is recommended, instead, to include 
a statement of the condition of the steam in the expression for 
steam consumption. 

The heat consumed by the engine may be figured from the 
total weight of steam supplied and the heat consumed from each 
pound. This latter expression requires consideration. Each 
pound of steam received by the engine carries heat in the form of 
latent heat and heat of the liquid. Part of this total heat is 
converted into useful work and part is lost to friction, radiation, 
etc., in the cylinder; the balance is rejected. During passage 
through the cylinder, part of each pound of H2O originally sup- 
plied is condensed, so that when it appears in the exhaust, it is 
partly water and partly steam at a considerably reduced pres- 
sure. The heat content of such a mixture is h'-\-x'L' (see page 140 
for notation), so that, properly speaking, the heat consumed by 
the engine is H — Qi' -\-x'L'), in which H is the total heat of the 



45 STEAM ENGINE TESTING 229 

steam supplied. That is, the heat consumed is the difference 
between the heat suppKed and the heat rejected. Of the heat 
rejected, however, the latent heat cannot be made use of without 
bringing in auxiliary apparatus such as a feed-water heater. 
Therefore it is reasonable to charge the latent heat of the exhaust 
against the engine. On the other hand, the heat of the liquid 
of the exhaust may be reclaimed if the exhaust is condensed 
and returned to the boiler. Therefore, a fair, though arbitrary, 
standard is 

for the heat consumed per pound of steam. Under ideal con- 
ditions the exhaust could be returned to the boiler as feed water 
without any drop of temperature; /i' may therefore be taken 
as the heat of the liquid corresponding to the pressure or tem- 
perature of the exhaust. This is the British standard and is 
to be preferred. The steam engine code of the A.S.M.E. rec- 
ommends that h be the heat of the feed water actually returned, 
but as this depends upon the power plant and not the steam 
engine, it seems less logical to use where results for the engine 
only are sought. 

If S is the weight of steam supplied per horse-power-hour 
in pounds, then the heat consumed per horse-power-hour is 

(a) Steam Consumption. Having measured the horse-power, 
it is only necessary to get the hourly rate of steam supplied. 
This may be done in various ways as follows. 

By Indicator Diagram. The engine itself makes a crude form 
of steam meter, since at every stroke a definite volume of steam 
is taken into the cylinder which can be measured from the 
indicator diagram. Referring to Fig. 32, page 51, at the point 
h cut-off takes place, the cylinder is closed to the boiler, and 
the cycle commences wath a volume of steam equal to that repre- 



r 



230 STEAM ENGINE TESTING 45 

sented by the point b. This comprises the clearance volume 
and the volume of the piston displacement up to the point 6, 
or {c+C)D cubic feet; c being the clearance expressed as a 
part of the piston displacement; C the cut-off expressed as part 
of the stroke, and D the piston displacement in cubic feet. 
Assuming the steam having this volume to be saturated, we 
may find its density in pounds per cubic foot from its pressure. 
Calling the density W, we have W{c+C)D lbs. as the weight 
of the steam at the point 6. Not all of this steam has been fur- 
nished by the boiler at the beginning of the C3Tle, however, 
since some steam from the previous stroke was compressed in 
the clearance space. Just before the valve opened to the boiler, 
the steam in the cylinder had a pressure and volume correspond- 
ing to the point e, Fig. 32. Its weight then is wcD, in which w is 
the density of saturated steam at the pressure at e. The amount 
of steam furnished by the boiler to one end each revolution is 
therefore W{c+C)D — wcD lbs. If N is the revolutions per 
minute, the weight per hour is 

60A^D{Tr(c+C)-u'c}.* 

This is the weight used on one end of the cylinder on the assump- 
tion that the steam is saturated just after cut-off. The weight 
on the other end may be found similarly. Now, the steam is 
not dry because of initial condensation, and it may have vary- 
ing degrees of wetness depending upon the cut-off, the work- 
ing range of temperatures, type of engine, etc. Numerous 
empirical formulas have been proposed for the calculation of 
cylinder condensation, an important item, since for simple 
engines it amounts to between 20 and 50 per cent of the amount 
of steam shown by the diagram. A method has been proposed 
by Professor J. Paul Cla>i:on which takes advantage of the law 
discovered by him that there is a definite relation between the 
amount of cylinder condensation and the exponent of expansion 

* See also foot-note, page 238. 



45 STEAM ENGINE TESTING 231 

in the equation Py'* = a constant, at all events for certain types 
of engines. (See Journal A.S.M.E., April, 1912.) He plots 
the indicator diagram on logarithmic coordinates (see Test 
41 (c)) and from the slant of the expansion line gets the value 
of n. By using a set of curves giving the quality of the steam 
in the cylinder just after cut-off at various values of pressure and 
??, the quality of the steam at cut-off and the cylinder condensa- 
tion may be calculated. These curves have not been sufficiently 
verified as yet to make them of general application. Further- 
more, the method seems to take no account of leakage of steam 
past the valve, which may never enter the cylinder, but is never- 
theless consumed by the engine. 

The clearance should be determined as described under 
Test 41. The expression for cut-off, C, may be found by divid- 
ing the distance of &, Fig. 32, from ae, by the length of the 
diagram, in inches. 

For the sampling of diagrams, see Test 10 (e). 

By Condenser. All of the steam used is passed into a surface 
condenser, and the condensate weighed for a counted time. 
This is probably the most accurate way of testing for steam 
consumption. Numerous time-quantity readings should be made 
to determine uniformity of flow. The condenser must be operated 
with more circulating water than is used in practice, so that 
the condensate will emerge cool; otherwise a large amount 
may escape unweighed by evaporation. The piping between 
the condenser and engine must be examined for tightness, and 
the condenser tested for leakage. The latter may be done 
by running the air-pump when no steam is flowing, and noting 
if any circulating water is drawn through, preferably when the 
condenser is hot. If it leaks a small amount, a leakage rate 
may be found and applied as a correction to the results. If 
the engine is to be tested '' non-condensing,'' that is, with 
no vacuum, the condenser must be vented in order to establish 
this condition. 



232 STEAM ENGINE TESTING 45 

By Steam Meter. One of the commercial forms of steam 
meter may be used in the steam pipe supplying the engine. See 
Test 30. 

By Feed-water Measurement. For this method, the engine 
and boiler supplying it should be isolated so that all of the steam 
generated by the boiler is used in the engine. Sometimes it 
is necessary to supph^ steam to auxiliary apparatus, such as a 
feed pump, from the boiler supplying the engine tested. In 
such a case, it is necessary to make a separate measurement 
of this steam, either by establishing the rate beforehand or, 
better, by condensing the steam used by the auxiliary during 
the test. It is necessary to examine the boiler and piping for 
tightness, the latter especially at branches stopped by valves. 
This is done by closing all valves in branches and the main 
stop valve at the engine so that the supply pipe is open from 
the boiler to the engine valve, but closed everywhere else. V^ith 
a quiet furnace fire so that there is no active evaporation, the 
level is then noted in the water column at a mmiber of uniform 
intervals of time. If the level falls, leakage is taking place, 
and the rate should be determined from the area of water surface 
calculated from the measurements of the boiler. This leakage 
may then l^e applied to the results of a test as a correction. 

The feed water may be measured by any of the methods 
given under Test 54. 

Willan's Law states that the weight of steam per unit of 
time used by an engine with a throttling governor varies directly 
as the indicated horse-power of the engine, very nearly'. The 
work represented by an indicator diagram in which the expan- 
sion follows the law that PT' = a constant (very nearly the case 
with steam) is mathematically proportional to the initial pressure, 
cut-off l)eing constant. As the pressure is proportional to the 
density of the steam, approximately, it follows that the weight 
of the steam is proportional to the work, and the indicated horse- 
power. The weight of steam used also varies directly with the 



45 STEAM ENGINE TESTING 233 

brake horse-power, since B.h.p. = I.h.p. — a constant. Experi- 
ment has shown that this relation applies not only to throttling 
engines, but to those of the cut-off type, and to steam tur- 
bines. 

The practical application of Willan's law lies in the conse- 
quence that if the weight of steam used per hour by an engine is 
plotted against its indicated or brake horse-power, the result 
is a straight line. This furnishes a check upon the results of a 
test as the test proceeds; if points so plotted do not follow a 
straight line, there is error. It should be noted that at over- 
loads, the curve is apt to deviate slightly from straightness, 
and lean toward the axis of steam weights. 

The duration of the test should depend upon the uniformity 
of conditions, the capacity of the engine, and the method used 
for measurement of the steam. During each test at a given 
load, weighings are made at uniform time intervals, say ten or 
fifteen minutes. When there are four to six of these of nearly 
equal amounts recorded consecutively, the run may be dis- 
continued, provided the error of starting and stopping is within 
reasonable limits. (See page 9.) This error depends upon the 
method of measuring the steam. If a condenser is used, the 
error will be relatively small, since it equals the difference in the 
amounts of condensate in the condenser at starting and stopping. 
If the boiler method is used, the test must be much longer, as 
there may be large error in the level of the water column, due 
to differences of density, ebullition, etc. With a steam meter, 
the test need be only long enough to get sufficient indicator 
diagrams for a fair average, provided the engine has been pre- 
viously given a settling run. 

Determinations of the condition of the steam supplied as to 
quality and pressure, and of the pressure or temperature of the 
exhaust, should be made and included in the statement of steam 
consumption per horse-power-hour. 

The relation between the steam consumption in pounds per 



234 STEAM ENGINE TESTING 45 

indicated horse-power-hour, Si, and per brake horse-power-hour, 
S2y is 

/Si = aS2 X mechanical efficiency. 

(b) Cylinder Condensation is often figured by subtracting 
the total steam used per hour, as shown by the indicator diagram, 
from that determined by direct measurement. The difi'erence 
includes not only cylinder condensation, but valve leakage in 
the case of engines which do not have separate valves controlling 
the exhaust. 

(c) Thermal Efficiency. There are two standards, one 
having a commercial, the other a scientific value. The former 
is the ratio of the heat equivalent of the useful work to the heat 
units consumed as defined under ^^ principles.^' Since there are 
S{H — h') heat units consumed for every horse-power-hour of 
useful work, and since the heat equivalent of a horse-power- 
hour is 2545 B.t.u., 

2545 



E = thermal efficiency = -^7 



S{H-h 



f\f 



in which S may be based on indicated or brake horse-power. 
If the former, the result is the '^ cylinder efficiency ''; if the latter, 
it is the ^* over-all efficiency.'' 

H may be obtained from the pressure and quality deter- 
minations of the steam supplied, by use of the steam tables; 
h is determined similarly from readings of a pressure gage or ther- 
mometer in the exhaust. 

The scientific standard is the Clausius efficiency, which is 
the ratio of the heat converted into work by the actual engine 
to that by an ideal one working without clearance space and with 
non-heat-conducting cylinder walls with cut-off early enough to 
allow expansion clear down to the back pressure. There will 
then be no clearance loss and the expansion will be adiabatic. 
The indicator diagram representing these conditions is shown 



45 



STEAM ENGINE TESTING 



235 



by Fig. 94, and is that of the Clausius cycle although it is more 
frequently referred to as the Rankine cycle. The initial pres- 
sure and quality of the steam and the back pressure are assumed 
to be the same in the ideal engine as 
in the actual. This is a more reason- 
able standard for efficiency than the 
commercial standard since the latter 
charges against the engine heat that 
it could not use under even ideal 
circumstances because of the limi- 
tations in the operation of the work- 
ing medium. 

To figure the Clausius efficiency it is first necessary to get 
the heat units that are converted into useful work from 1 lb. 
of steam under actual conditions. This is 




Fig. 94. — Clausius Cycle. 



E{H-h'). 

Under the conditions of the assumed ideal engine the heat con- 
verted into work is the difference between the total heat H of 
the steam supplied and the total heat of the exha.ust Hij since 
there are no losses. Hi is the theoretical amount of heat left 
in a pound of steam after it has expanded adiabatically from the 
given pressure and condition as to quality to the given back 
pressure. It may be calculated by the use of entropy tables, 
but it is more convenient to get it directly from the Mollier 
total heat-entropy diagram which gives the heat of steam under 
all conditions and at various stages of adiabatic expansion. Hav- 
ing found Hij the Clausius efficiency is obtained from the relation 



Ec = 



E{H-h') 



H-Hi • 



Another way of figuring this efficiency is to divide the steam 



236 STEAM ENGINE TESTING 45 

consumption of the ideal engine, Scy in pounds per horse-power- 
hour, by that of the actual engine, aS. 



Sc^ 2545 1 
S ~H-HiS' 



This is a useful form, since by it the cylinder or over-all efficiency 
may be readily obtained, depending upon the basis of S. 

Problem 45i. An indicator diagram shows the cut-off to be one-fifth of 
the stroke. The pressure at cut-off is 110 lbs. abs.; at the end of compres- 
sion it is 25 lbs. abs. The engine is 10 in.Xl2 in. X 100 R.p.m., single acting 
with 4 per cent clearance. How many pounds of steam are supphed per 
hour, allowing 25 per cent of that shown by the diagram for condensation? 

Ans., 233. 

Problem 45:. If the mean-effective pressure in the preceding is 25 lbs., 
what is the steam consumption in pounds per I. h. p. -hour? Ans.y 39.2. 

Problem 45.> If the steam in the supply pipe (last problem) is at 105 
lbs. gage and contains 3 per cent of moisture, and if the exhaust is at 3 lbs. 
gage, what is the thermal efficiency? Atis.^ 6.69%. 

Problem 45;. What is the Clausius efficienc}' for the foregoing? 

Ans., 48.1%. 

Problem 455. Deduce from the topical form of Willan's line, the form 
of the curve between steam consumption in pounds per B.h.p.-hour and 
B.h.p. What is the value of the steam consumption when B.h.p. =0? 



46. Test of a ^Multiple Expaxsiox Engine 

Principles. The results to be sought are in part identical 
to those for a simple engine; hence the principles under Tests 
44 and 45 are appropriate and should be read in this connec- 
tion. In addition, there are other data useful to the study of 
multiple expansion, principally pertaining to the indicator dia- 
grams. The sampling of diagrams is therefore very in portant, 
and should be done according to Test 10 (e). 

Although, for brevity, a compound engine only will be con- 
sidered here, the methods apply equally to any multiple expan- 
sion. 



46 STEAM ENGINE TESTING 237 

(a) I.h.p., B.h.p., F.h.p., and Mechanical Efficiency may be 
found as for a simple engine, but in many cases the unit will 
be too large to brake conveniently, or a generator connection 
will make that procedure impossible. 

In the former case, the F.h.p. may be determined by run- 
ning the engine free and taking indicator diagrams, called under 
these circumstances ^' friction diagrams.'' The I.h.p. from such 
diagrams equals the friction horse-power. If the F.h.p. is 
assumed constant at all loads, this single determination of it at 
zero load enables the calculation of the B.h.p. at any load, 
since 

B.h.p. = I.h.p. -F.h.p. 

When there is a direct connected generator, the electrical 
load should be measured as for a steam turbine (Test 47 (a) ). 
If the efficiency curve of the generator is known, the B.h.p. of 
the engine may then be closely estimated. 

The I.h.p. may be obtained by figuring that for each cylinder 
separately, and adding them to get the total I.h.p. Or the 
'^ equivalent mean effective pressure '' (to be defined later) may 
be used in a single calculation upon one cylinder. 

Whenever possible, the B.h.p. should be used as the inde- 
pendent variable (if results from the engine alone are to be 
considered). 

(b) Steam Consumption by condenser, steam meter, or 
feed-water measurement. See Test 45 (a). 

(c) Thermal Efficiency. See Test 45 (c). 

(d) Equivalent and Aggregate M.e.p. The equivalei* c 
M.e.p. referred to any cylinder may be defined as a pressure of 
such value as to produce the same horse-power in the referred 
to as in the actual cylinder. Thus, 

Let Ah and Ai = net piston areas for high- and low-pressure 

cylinders, respectively. 



► 



238 STEAM ENGINE TESTING 46 

Ph and Pi = the M.e.p.'s, high- and low-pressure cylinders, 
respectively. 

Then the M.e.p. of the high-pressure C3'linder, referred to the 
low, is 

and the M.e.p. of the low-pressure cylinder, referred to the 
high, is 

The combined or '^ aggregate ^' M.e.p. is one of such value 
that, if it prevailed in the cylinder referred to, there would be 
produced in that cylinder an I.h.p. equal to that actually pro- 
duced by all cyhnders. That is (calling the aggregate M.e.p., 

Referred to the H.P. cyhnder, Pm = Pn+^XPi. 



Referred to the L.P. cylinder, Pin = PhX-^+Pi. 

and similarly for three or more cylinders. 

(e) Steam Accounted for by Indicator Diagrams. On p. 
230 is Reduced the relation that the weight of steam per hour 
shown by an indicator diagram equals * 

60X D{W{c+C)-wc}. 
Now, for a single cyhnder engine, 

PLaN PN(DIU) 



I.h.p. = 



33,000 33,000 



* This formula is sometimes quoted with ic{c-\-k) in place of wc, c+k 
then standing for the volume of the steam at the beginning of the compres- 
sion curve 



46 STEAM ENGINE TESTING 239 

Dividing the one equation by the other, we have 

Wt. of steam per H.p.-hour = — ~ — {W{c+C) — wc)y 

in which P is the mean effective pressure, c and C are the 
clearance and cut-off volumes expressed as parts of the piston 
displacement, respectively; and W and w the densities of satur- 
ated steam at the pressures of cut-off and compression, respec- 
tively. This last equation is the more convenient form for the 
diagram water rate. 

The procedure then is to measure C, TF, and w on repre- 
sentative diagrams (c being known) from the cylinder considered. 
The aggregate M.e.p. referred to that cylinder (defined under 
(d) ) is then calculated and taken as the value of P in the 
water rate formula. The result is the steam accounted for by 
the diagram from the cylinder considered. The procedure is 
repeated for the other cylinders. 

(f) Combined Diagram. Let 

Dh and A = piston displacements, cu. ft., of high- and-low pressure 
cylinders, respectively. 
Vh and IV = clearance volumes, cu. ft., of high- and low-pressure 
cylinders, respectively. 

Select representative diagrams from the cylinders, as in Figs. 
95 and 96, and divide them into ten or more equal spaces by 
vertical lines. 

Choose convenient scales of pressure and volume for the com- 
bined diagram. Fig 97, and lay them off on coordinate paper. 
Draw in the atmospheric pressure line. 

Locate the vertical line 1-2, Fig. 97, at the volume graduation 
corresponding to the clearance volume, Vi. Locate the vertical 
3-4 at the volume graduation corresponding to Vi+Di. 

Make ten (or more, corresponding to Fig. 95) spaces between 
lines 1-2 and 3-4 with equidistant vertical lines. 



240 



STEAM ENGINE TESTING 



46 



























2/ 








22 


> 


B 


o'lle 


r Pressure 


*. ' " LT "^TT-, 


1 

\ 
\ 
\ 


15 


16 


" 




\ 


CIO 


<"Zero Volume ' 


21 24 X--V /4.7/b. 


1 1 — —^^. 

/2 1 \Bo'ilerPn Fig. 96.— H. P. Diagram. 






Tifr- 


>> \ 




i 

II 






\ \ 


1 r ' ' 


i. 


\ \ 2 


^! Q 


7 > 




l] 








\ \ 


I 




X 




i 1 


i 

1 






V \ 








TS^ /4.7/d. 


I i 


, 1 






"">^-TN 












\ \ V 












■ ■ \ 












;\ '< > 






i 




1 \ 


1 \| \ ,^^ 


" 








, 


\ \ Condenser Pressure-^ 




i 










\ \ Fig. 95.— L.P. Diagram. 




1 , 












\\ 




\ 












A \ 




\ 1 










;\ \ 




\ 1 








1 




' 


V \ 




V| 
















\ . \ 




V 
















\iA 


T \ 




\ 


1 






\l 


\ 


// T 










1 


3 \ 


1 


II.- 7 


' \ 


1 \ 


» 


\ 


2 


^: b 7\ ' 












\ 






1 




V \ 










N. ^ 










\^ 


\^ 





__U_i._i_J__. 


^ 




1 
^1 


1 


1 








"r\h 


-^1 ' — n ' ^ T- ■ T T ■ r ■ 'i conaen:)(fr rr. 

•» -♦- i — — 


zero Pr 



Fig. 97. — Combined Diagrams from a Compound Engine. 



46 STEAM ENGINE TESTING 241 

Points 5, 6, 7, etc., on the reconstructed diagram may now be 
located on these verticals by scaling the pressures of the corre- 
sponding points of Fig. 95 from the atmospheric line. In this 
way the full low-pressure diagram may be reproduced on the com- 
bined diagram. 

Locate vertical 11-12, Fig. 97, to represent the clearance 
volume Vh] and 13-14 to represent Vn+Dn^ 

Draw equidistant verticals between 11-12 and 13-14, and 
locate points 15, 16, 17, etc., as for the low-pressure diagram. 
This establishes the high-pressure diagram. 

The combined diagram. Fig. 97, fairly represents the whole 
expansion of the steam on a single P-V scale. When making 
comparisons with assumed ideal expansion diagrams, however, it 
should be borne in mind that Fig. 97 does not truly represent the 
continuous expansion of a given weight of steam. The high- 
pressure expansion curve is for all of the steam in the high-pressure 
cylinder; but the low-pressure expansion is for a lesser quantity 
of steam by the amount caught in the clearance of the high- 
pressure cylinder. Furthermore, valve and piston leakage will 
affect the validity of comparisons made with the hyperbolic ex- 
pansion curve or the constant steam weight curves. 

To draw in the ideal expansion line for the given conditions 
(the ideal being assumed hyperbolic, or PF = a constant), the 
boiler pressure line should first be drawn in on both the high- 
pressure and combined diagrams, as indicated on Figs. 96 and 97. 
The compression line of the high-pressure diagram (Fig. 96) is 
continued on a hyperbolic curve until it intersects the boiler 
pressure line at point 21. The expansion curve is continued 
similarly, thus locating point 22. The volume corresponding to 
the distance between 21 and 22 is now calculated in cubic feet. 
This volume is assumed to be that of the steam received from 
the boiler per stroke, as though in an engine without clearance. 

Now continue line 1-2, Fig. 97, until it intercepts the boiler 
pressure line at 23. From 23 lay off 23-24 equal to the volume 



242 STEAM ENGINE TESTING: 46 

just calculated. Through 24, construct the required hyperbolic 
curve by one of the well-known methods, using the hne 1-2 and 
the condenser pressure line as zero axes. 

(g) The Ratio of Expansion is equal to the volume of the low- 
pressure cylinder, including clearance, divided by the volume of 
the steam in the high-pressure cy.inder, including clearance, 
at the point of cut-off. The last named is found as follows and 
is then termed the ^' commercial cut-off/' Referring to the high- 
pressure diagram, Fig. 96, a horizontal is drawn through the 
highest point on the steam admission line. The intersection of 
this horizontal with the prolonged expansion curve, that is point 
26, is the commercial cut-off. 

(h) The Diagram Factor may be found by dividing the area 
of the combined diagram. Fig. 97, by the area of the ideal diagram, 
23-24-25-4-3-1. Or it may be calculated by dividing the aggre- 
gate M.e.p. referred to the low-pressure cylinder by the ideal 
M.e.p. obtained from the following formula: 

Ideal M.e.p. =^(1+Iogei20-P, 
K 

in which P' = boiler pressure, lbs. per sq. in., absolute; 

p = condenser pressure, lbs. per. sq. in., absolute; 

^, . , , ,. . . length 1-3 

it = ideal ratio of expansion = , ° ^^ ^ . , 

^ length 23-24 

47. Economy Test of a Steam Turbine 

Principles. The measurements and results, in general, are 
the same as those for a reciprocating engine, except that there 
can be no indicated horse-power determination, and often no 
brake measurements, an electrical load being considered instead. 
Since it is not possible to indicate a turbine, the term ^^ internal 
horse-power '* is sometimes used to express the equivalent of 
indicated horse-power, but it is not a definite quantity. It is 



47 STEAM ENGINE TESTING 243 

often impracticable to apply a brake to the turbine shaft on account 
of the direct connection of a generator; in such a case the tur- 
bine and generator must be tested as a single unit. For other 
details, see Test 45, principles. 

(a) Determination of the Useful Horse-power may be made 
the same as for Test 44 if the turbine alone is tested with the 
use of a brake. Otherwise, the electrical load should be measured 
in kilowatts by taking either wattmeter readings or readings of 
amperes and volts. The horse-power equivalent to the electrical 
output, that is, the ^' electrical horse-power, '^ may be found from 

1 Electrical horse-power (E.h.p.) =0.746 kilowatt. 

For alternating current generators, the code of the A.S.M.E. states 
that the electrical output is the kilowatts delivered to the switch- 
board less that required for field excitation when the field is 
separately excited. Under this condition, therefore, measure- 
ments of the field current and voltage should be made. 

(b) Steam Consumption. The pounds of steam consumed 
per hour may be measured by any of the methods described 
under Test 45 (a) except by indicator diagram. Dividing this 
by the kilowatts or horse-power gives the pounds of steam per 
kilowatt- or horse-power-hour. 

It is often desirable, for purposes of comparison, to base 
the steam consumption on brake horse-power or ^^ internal horse- 
power.'' The former quantity may be estimated, if an effi- 
ciency curve of the generator is available, by multiplying the 
steam consumption in pounds per electrical horse-power-hour 
at a given load by the generator efficiency at that load. 

The internal horse-power is difficult to estimate with any 
degree of accuracy. It is sometimes assumed to be the quo- 
tient of the brake horse-power and the mechanical efficiency of a 
steam engine working under the same conditions. This, of 
course, is a crude estimate. Using it, however, the steam con- 
sumption may be expressed on the basis of internal horse-power. 



244 STEAM ENGINE TESTING 47 

For duration of the test, see page 233. 

Additional Data. If there are traps arranged to catch con- 
densation from the turbine casing, they should be drained regu- 
larly and the condensate weighed in with the steam consumed. 
Readings should be made of the pressure in the nozzle chamber 
to show the drop of pressure through the governor valve. If 
this drop is excessive, the steam consumption will be correspond- 
ingly high. The predetermined conditions of pressure, quality, 
and back pressure or vacuum should be kept as constant as 
possible, and the Cjuantities carefully measured, as they have a 
decided influence upon the economy of a turbine. It is impor- 
tant that the barometer be read to get the required accuracy 
in the measurement of vacuum which should be expressed as an 
absolute pressure. This is because at low pressures the heat 
content of steam varies materiall}' with the pressure, and also 
because turbine economy is more dependent upon the predeter- 
mined vacuum than pressure or superheat. 

For the purpose of estimating the steam consumption of a 
turbine under a given set of conditions of steam pressure, quality 
and vacuum, such as are stated in the manufacturer's guarantee, 
the turbine being tested under somewhat different conditions, 
correction curves are suppHed by the manufacturer. These 
show the number of pounds of steam per horse-power- or kilo- 
watt-hour to be subtracted from the test result if the stated 
pressure is higher than the actual, the number to be subtracted if 
the stated superheat is higher, and the number to be subtracted 
if the stated back pressure is lower, or vice versa. 

Willan's line should be plotted during all trials under vari- 
able output. 

(c) The Thermal EflBciencies are obtained exactly as for 
Test 45 (c), the basis for the computation of useful work being 
the electrical, brake, or internal horse-power. 

(d) Separation of Losses. The losses of a turbine ma}- be 
considered in two groups. First, approximately constant losses 



47 STEAM ENGINE TESTING 245 

which include those due to friction and radiation Frictional 
resistance is encountered at the bearings and stuffing boxes, and 
between the discs and blades and the steam, and through wind- 
age of the external parts. Second, steam losses including leakage 
through clearance spaces, condensation, and faulty action of 
the blades and nozzles in not completely absorbing the energy 
of the steam. 

These losses may not be separately measured without an 
involved test. Professor Carpenter has indicated a method of 
separating the two groups by the use of Willan's line. When 
plotted against brake horse-powers, this line intercepts the axis 
of steam consumption at a point w^hich shows the steam con- 
sumed per hour to overcome the first group of losses, that is, 
at no load. The distance parallel to the load axis, measured in 
horse-power, necessary to move Willan's line so that it shall pass 
through the origin, equals the power given to the first group of 
losses. At any other load, this quantity is to be subtracted from 
the power that would be developed by the actual amount of 
steam consumed if operating on the Clausius cycle; the result 
is the actual brake horse-power plus the second group of losses, 
from which the second group may be readily obtained. 

Problem 47i. A turbine, tested at full load, consumes 3150 lbs. of steam 
in 90 minutes. The current delivered is 340 amperes and 220 volts. The 
generator efficiency at full load is 95 per cent and the friction losses of the 
turbine are 5 per cent of the power deUvered to the generator. What is the 
steam consumption in pounds per kilowatt-hour, per E.h.p.-hour, per B.h.p.- 
hour, and per internal horse-power-hour? Arts., 28.1 per Kw.-hr. 

Problem 472. For the test of Problem 47i, average values as follows 
were obtained. Steam pressure, 150 lbs. gage; superheat, 80° F.; vacuum, 
20 inches mercury; barometer, 28.5 inches. What would have been the steam 
consumption if the following conditions held? Steam pressure, 180 lbs., 
abs.; superheat, 100° F.; vacuum, 28 ins.; barometer, 30 ins. Correc- 
tions are 0.05 lb. per kilowatt-hour for each pound difference in the steam 
pressure, 0.02 lb. for each degree of superheat, and 1.0 lb. for each inch of 
vacuum. Arts., 20.5 lbs. per Kw.-hr. 

Problem 473. What is the efficiency (British standard) for the results 
of Problem 47i? How much efficiency should be added or subtracted for 
each unit of steam pressure, back pressure, and superheat. (See Problem 472.) 



246 STEAM ENGINE TESTING 48 

48. Economy Test of a Steam Power Plant 

Principles. A complete test consists of measurements of the 
amounts of heat distributed and lost in the entire system, 
beginning with the energy of the fuel and ending with the energy 
delivered at the shaft or switchboard. For the present we shall 
consider only that part of the plant beyond the boiler, the subject 
of boiler trials being separately treated under Test 54. 

The most important result from power plant tests is the fuel 
consumption in pounds of fuel per horse-power- or kilowatt- 
hour. Other results are the steam and heat consumption of the 
engine and the auxiliaries, and the heat balance. The latter is 
an equation between the total heat available and the various 
amounts accounted for in its distribution. They may be found 
in heat units per hour and expressed as per cents of the total 
heat per hour added to the feed water entering the boiler. If 
tliese percentages are separately multiplied by the boiler efficiency, 
the items of the heat balance will then be percentages of the heat 
available in tie fuel. This follows from the fact that boiler 
efficiency is that part of the fuel energy which is added to the 
feed water and distributed as steam. 

The boiler trial, which is part of the complete test and con- 
ducted at the same time, gives the efficiency of the boiler and its 
losses, all based on the heat value of the fuel. A complete 
heat balance is thereby obtainable. 

The usual condensing power plant contains as auxiliaries a 
condenser, circulating pump, air pump, and feed water pump. 
There may also be a cooling tower and its auxiliaries, and a feed 
water heater using the exhaust steam from the auxiliaries, and 
such minor apparatus as separators, traps, etc., wliich may or 
may not be arranged to drain back to the boiler. 

The rearrangement of the apparatus and piping for the pur- 
pose of testing should interfere as little as possible with normal 
operating conditions, and any departures from them that may 



48 STEAM ENGINE TESTING 247 

effect the results, such as different feed water temperatures, 
should be allowed for by making a separate test to measure the 
actual working quantities that have been altered. " , 

Equipments of different power plants are too varied for very 
specific directions for the measurements of the various quan- 
tities. Any of the methods given under Test 45 (a) for the 
measurement of steam weights should be applied according to 
the exigencies of the particular test. Any one item of the heat 
balance may be omitted from the direct measurements, since 
one item may always be figured by subtraction. 

The basis of all heat measurements is the heat contained by 
the feed water just before it enters the boiler or economizer if 
there is one. 

Duration. If a boiler trial is included, its duration deter- 
mines the length of the test; if the engine and auxiliaries only are 
to be tested, the duration should be the same as for a test of the 
engine alone. See Tests 45 and 54, principles. 

(a) Steam and Heat Consumption of Engine and Auxiliaries 
per Horse-power- or Kilowatt-hour. Let w stand for weight 
of steam per hour; H, for its total heat per pound above 32 degrees 
depending upon its pressure and quality; and let h be the number 
of heat units per pound of the feed water above 32 degrees. Let 
the subscripts e, c, a, /, and b refer to the engine, circulating 
pump, air pump, feed pump, and boiler respectively. Then 
the steam consumption is 

(we+Wc+Wa+W/) -T-horse-power or kilowatts output. 

To get the heat consumption, the various values of H should 
be used for strict accuracy, as determined by the pressure and 
quality of the steam just before it is delivered to each unit, but 
in most cases the following form is practically correct. 

Heat consumed per hour = We{He — h) + {wc+Wa+Wf)(Hb — h) . 

Dividing this by the horse-power or kilowatts gives the 
required quantity. 



248 STEAM ENGINE TESTING 48 

The heat consumed per hour by the engine and auxiharies 
may also be determined by subtracting the heat lost to leakage 
and drips from the total heat added to the feed water (see (6) 
and (c) following). 

The values of H should be obtained from the steam tables 
by reference to the measurements of pressure, temperature, 
and quality of the steam at the point considered. For Hb this 
should be immediately beyond the main stop valve of the boiler; 
for Hej it should be just behind the main stop valve of the engine, 
between it and the separator if one is used, h is obtained from 
the temperature of the feed water just before it enters the boiler. 
If an injector is used, the temperature should be taken before 
entering the injector, since the heat added by that instrument 
comes from the boiler and returns to it. The heat consumed 
by the feed pump in this case should be figured separately and 
is very nearly equal to the heat equivalent of the work done in 
pumping. (See Test 52.) 

(b) Heat Added per Hour to the Feed Water. If there is 
only one source of supply yielding W lbs. per hour, then the heat 
added is 

W{Hi,-li), 

If in addition to this there is another supply such as would be 
obtained from traps, separators, etc., draining back to the boiler 
in an independent pipe carrying Wo lbs. per hour, then the heat 
added is 

Wi{Ih-li{) + W2{Hr,-h2), 

the subscripts 1 and 2 referring to the main and auxiliary supplies, 
respectively. 

The quantities Ih and h are measured as under («). The 
weight of the main supply is generally measured by a weighing 
system as for boiler trials (see Test 54 (6)). Auxiliary supplies 



48 STEAM ENGINE TESTING 249 

of feed may be metered or directly weighed during a special 
test made for that purpose. 

(c) Heat Lost to Leakage and Drains. Leakage may occur 
from the steam space of the boiler or from the steam pipes either 
to the air or to pipe branches, and it m.ay occur below the w^ater 
level in the boiler. Leakage wdnch cannot be prevented should 
be measured by a preliminary test similar to that described on 
page 231 for leakage correction. It is assumed that the rate of 
leakage thus determined remains the same through the test of 
the plant. Calling it wi pounds per hour, the heat lost is 

Wi{Hb — h) 

If the separators, traps, etc., do not drain back to the boiler, 
they may be kept closed during the test and drained at regular 
intervals into buckets of cold water whereby they are w^eighed. 
If Wd is the number of pounds of w^ater wlthdraw^n per hour, 
the loss is 

iVd{Hb — h) 

If this water is returned as an auxiliary supply, /i2 should be 
substituted for h in the above. 

(d) Heat Balance. All the items, having been measured as 
above in heat units per hour, may now be expressed as percentages 
of the heat added to the feed w^ater. Then the heat balance is 

100% = % of heat consumed by engine 

+ % of heat consum.ed by auxiliaries (stated sepa- 
rately or collectively) 
+% of heat lost to leakage and drains. 

The first item on the right-hand side may be subdivided into the 
per cent of heat equivalent to the useful work and the per cents 
representing the various engine losses. 

It should be noted that this method of analyzing the heat 



250 



STEAM PUMP TESTING 



49 



distribution charges against the engine and auxiUaries the losses 
of radiation between the condenser and the boiler. Also, if a 
feed water heater is used, the heat consumed by the engine 
figures less, although the actual performance of the engine is 
exactly the same as if no heater were used, because the value of 
hj the heat of the feed water, is higher. The only way in which 
the effect of the heater appears numerically is in the heat added 
to the feed water, but no idea of the saving due to the heater 
may be formed. 

Problem 48i. A condensing plant is arranged so that the exhaust from 
the auxiliaries preheats the feed water after it leaves the condenser, in a closed 
heater. Tell how the phmt could be tested so as to show the loss due to drop 
in the heat of the liquid between the engine exhaust and the heater entrance, 
and the gain due to the feed water heater. 



49. Valve Setting of a Duplex (Steam) Pump 

Principles. The duplex pump consists of two reciprocating 
steam pumps operating side by side and arranged so that the 
piston rod motion of one operates the steam valve of the other. 
Each pump consists of a water cylinder whose piston is directly 
driven by the piston rod of the steam cylinder. 

The steam valves distribute the steam so that one pump is 
on its forward stroke when the other is on its return. The valves 

have neither laps nor lead, so 
that cut-off occurs simultane- 
ously with release. The valve 
stem of each pump is driven 
by a rocker deriving its motion 
from the piston rod of the other 
pump (see Fig. 98). As each 

Fig. 98.— Duplex Pump Valve-Motion, rocker moves through the 

whole piston rod stroke and as 
it is desirable that the valves throw only at the end of the stroke, 
a certain amount of lost motion is provided between the valve 




49 STEAM PUMP TESTING 251 

stem and the valve. This is shown by the distance c in the 
figure. The valve stem passes freely through a hole in a lug on 
the valve, and gives motion to the valve only when the nuts n 
and n come into contact with the lug. By adjusting the lost 
motion, the valve may have more or less throw. 

There are two steam and two exhaust ports for each steam 
cylinder, SS and EE, This is arranged as a safeguard against 
the piston hitting the cylinder head. If the valve should not 
close the exhaust port before the end of the exhaust stroke, the 
piston itself will close it, thus entraining steam in the clearance 
space which acts as a cushion. 

(a) Adjustment of Lost Motion of Valve. This is accom- 
plished by setting the valves in their mid-positions when the 
pistons are in their mid-positions. 

The pistons should be set by reference to prick marks on the 
piston rods. The limiting positions of stroke should be meas- 
ured by prying each piston rod with a bar to the extreme of its 
travel, pressure behind the pistons being released by opening 
drains or otherwise. When the piston rods are set midway 
between these positions, the rockers should be vertical. 

With the steam chest cover removed, the valves are now 
placed so that they completely cover the ports. The nuts n, 
n, Fig. 98, are then adjusted so that there is an equal amount of 
clearance between each one and the valve lug. With some 
designs, there is only one nut to be adjusted on each stem, this 
nut then being between two lugs. In such a case the clearances 
may not be changed in amount, but only equalized. In other 
designs there is a ^^ lost motion link '' outside of the valve chest 
by which the clearances may be adjusted without opening the 
chest. 

The proper amount of clearance depends upon the size and 
design of the pump and may be determined by trial. If the steam 
ports are to be opened full each stroke, then the total lost motion 
should be equal to the throw of the valve stem corresponding to 



252 STEAM PUMP TESTING 50 

normal piston stroke less twice the steam port length parallel 
to the stroke. 

(b) Readjustment after Trial. If, after the valves are set, 
the pump runs ^' lame,'^ that is, the strokes are unequal in 
length or time, it may be because the resistances of the water 
cylinders are different. They should then be examined for 
leaky water valves, tight stuffing boxes, etc. Such faults being 
corrected, if the pump still runs lame, the lost motion of the 
valves must be readjusted until the desired equality of strokes 
is obtained. It need only be remembered that to diminish the 
lost motion makes the valve throw greater, thus providing 
better access to the steam and release to the exhaust. 

Problem 49i. Explain why the ordinary duplex pump cannot use steam 
expansively. 

Problem 492. If the stroke of one piston rod of a duplex pump were 
curtailed at the head end, being normal in other particulars, what should 
be done to the valve motion to remedy it? 



50. Mechanical Efficiency Test of a Reciprocating 

Steam Pump 

Principles. The mechanical efficiency of a steam pump 
equals the useful or water horse-power, W.h.p., divided by the 
indicated horse-power of the steam cylinders. If D is the 
total head in feet pumped against, including suction and dis- 
charge, and W is the number of pounds of water delivered per 
minute, then, 

^^•^•^^• = 33;000^ 

If there were no leakage of water in the pump from one side 
of the piston to the other or through the valves, then the work 
done per minute would be equal to the product of the total 
pressure pumped against in pounds per square foot and the volume 



50 STEAM PUMP TESTING 253 

displaced by the piston in cubic feet per minute. If p stands 
for the pressure in the discharge pipe; p\ for tlie vacuum in 
the suction pipe, both in pounds per square inch ; and if L and 
A are the same as in the formula for indicated horse-power, and 
N is the number of working strokes per minute, then 

lU(p+v^)LAN 
'^ ^^' 33,000X144 • 

On account of leakage this formula is not a reliable one with 
which to determine the water horse-power. It may be used only 
by assuming a value for the leakage, and this may be very inexact. 

Leakage of water in a pump, of the kind referred to, is called 
^^ slip.'' It is generally expressed numerically as a percentage 
of the piston displacement. 

(a) Steam End Indicated Horse-power at Various Water 
Horse-powers. The indicated horse-power is found exactly 
as for a steam engine (see Test 44 (a)), except in regard to measure- 
ment of the stroke length, L. With direct acting reciprocating 
pumps, there is no constant limit to the stroke length and in 
ordinary operation it may vary materially. An average value 
should therefore be obtained from a number of measurements 
throughout the test. There is on the market a continuous 
recording device for this purpose, but if one is not available, the 
average stroke may be obtained from the average lengths of the 
indicator diagrams, the ratio of reduction being known. Another 
method is to set a scale against a mark on some projecting part 
of the piston rod, and to note the travel of this mark at regular 
time intervals. 

The w^ater horse-power may be varied either by changing 
the speed of the pump or the discharge pressure. With reciprocat- 
ing steam pumps, the pressure is usually approximately constant, 
and the water load varies with the quantity of water demanded. 
Either the pressure or the speed may be the independent variable 
during test, according to the operating conditions of the pump. 



254 STEAM PUMP TESTING 50 

The pressure may be varied during the test for different 
runs, by opening the stop valve in the discharge pipe more or less. 

The quantity of water delivered per minute may be measured 
by any of the methods of determining water rates. For large 
pumps, weirs may be used. 

The head against which the water is discharged may be 
measured with a pressure gage set in the discharge pipe.* The 
suction head generally may be measured in feet, and taken as 
the difference in level between that of the water supplied and the 
center of the pressure gage used for micasuring discharge pressure. 
Since 1 lb. per square inch = 2.3 feet head, the total head is 

in which Z)' is the suction head in feet. 

Readings of p and D' should be taken at regular intervals 
during each run. 

These quantities determine the water horse-power according 
to the formula previously given. The water horse-power may 
be estimated, according to the second formula, if the discharge 
pressure and the number of strokes per minute are measured, 
and if a value for the percentage of slip is assumed (see (rf)). 

Neither of the formulas for water horse-power takes into 
account the kinetic energy of the water delivered. Generally 
the velocities of the water are low enough to make this a negligible 
quantity. If it is desired to calculate the horse-power due to 
kinetic energy, the velocity should first be figured from the 
cubic feet discharge per unit of time and the cross-section of 
the pipe. The result is then obtained ])y, 

W.h.p. available from kinetic energy = -^ ^33,000 

in which W has the same value as before, v is the velocity in feet 
per second, and r/ = 32.2, nearly. 

* See also Test 70 (c). 



60 STEAM PUMP TESTING 255 

(b) Mechanical and Fluid Losses. The loss due to mechanical 
friction of the pump parts may be obtained b}^ indicating both 
the water and steam ends of the pump. The indicated horse- 
power of the water end is obtained in exactly the same way as ' 
for the steam cyhnder, the same values being used for the num- 
ber of strokes per minute and the average length of stroke. 
Then the steam end I.h.p. minus the water end I.h.p. equals 
the mechanical friction horse-power. 

The fluid losses are due to leakage, or slip, fluid friction 
of the water against its passage in the por!:s, eddies, etc. Slip 
causes loss of power through water being pumped against pres- 
sure from one part of the pump to another without being dis- 
charged into the delivery main. These losses are included in 
the power shown by the indicator diagram for the water end. 
Consequently the horse-power lost equals the I.h.p. of the 
water end minus the W.h.p. as calculated under (a). 

(c) The Gross Efficiency for each value of W.h.p. is obtained 
by dividing the W.h.p. by the corresponding I.h.p. of the steam 
end. It is sufficient, for each run, to use average values 
of heads, water rates, mean effective pressures, and stroke 
lengths and speeds with which to calculate a single value of 
efficiency. 

The indicated horse-power of the water cylinders is some- 
times measured. This divided by the I.h.p. of the steam 
cylinders is the efficiency covering mechanical losses only. 

(d) Slip. The piston displacement in cubic feet is "T7T" 

per minute. The water actually displaced, in the same units, 
is Tr/62.5 at ordinary temperatures. The percentage of slip 
is therefore, 

LAN W_ 

144 62.5^^^^^ ^__ ^^Q^^ 



LAN 
144 



\ LAN) 



w -^■' 



256 STEAM PUMP TESTING 50 

The quantities involved have been obtained for the other 
determinations. 

(e) The Capacity of pirnips is generally expressed in gallons 
per twenty-four hours. Knowing the weight of water, or cubic 
feet, discharged per minute, the capacity is readily calculated, 
for which purpose the following closely approximate relations 
may be used. 

1 gal. weighs 8.33 lbs. i cu.ft. contains 7.5 gal. 

Problem 50i. The follo^^-ing data are obtained from the test of a duplex 
pump. Discharge pressure, gage, 35 lbs.; suction lift, 4.5 ft.; water dis- 
charged per minute, 110 lbs.; length of stroke, 5 ins.; number of strokes 
per minute, both cylinders, 250; size of water cylinders, 2 ins.Xo ins. 
What is the W.h.p., the percentage of slip, and the capacity of the pump? 

An^., 0.283 H.p.; 22.6%. 

Problem SOo. In the preceding problem, if the internal diameter of the 
discharge pipe is 1.38 ins., what is the horse-power due to velocit}'? 

Problem 5O3. If the pressure in the discharge pipe is 12 lbs., and if the 
water supply is 6 feet above the gage indicating the discharge pressure, what 
is the total head? Am., 21.6 ft. 

Problem 50> Run a series of tests on a steam pump to show the rela- 
tion between slip and discharge pressure, and slip and speed. 



51. Economy Test of a Stea:ii Pump 

Principles. These, in general, are the same as given for the 
economy test of a steam engine, Test 45, the only difference 
being that the useful work is measured in terms of water horse- 
power as defined under Test 50. 

In addition to the measurements listed under Test 45, 
another one is usually required, namely, of '^ duty/' Duty is 
the number of foot-pounds of useful work performed by a pump 
per miUion B.t.u. consumed by the engine. 

(a) Steam and Heat Consumption. The pounds of steam 
consumed per hour may be found by any of the methods under 
Test 45 (a). The water horse-power is determined as under 



51 STEAM PUMP TESTING 257 

Test 50 (a). From these two quantities the pounds of steam 
per W.h.p.-hour may be calculated. 

The heat consumed per pound of steam is H — h\ using the 
same notation and reasoning as given under Test 45, principles.' 
Pressure readings of the supply and exhaust steam, and quality 
determinations of the supply steam are required for these heat 
quantities. 

(b) Thermal Efficiency. This is the same as for Test 45 
(c) except that the British standard only need be used in most 
cases. 

(c) Duty. The thermal efficiency (British standard), when 
expressed as a fraction, is the heat equivalent of the useful work 
done per B.t.u. consumed. The number of foot-pounds of usefui 
work done by each B.t.u. consumed is therefore 778 times the 
efficiency, 778 being the mechanical equivalent of heat. Since 
the duty is the number of foot-pounds per milhon B.t.u. consumed, 

Duty = 778,000,000 X Efficiency. 

It should be noted that the efficiency is here expressed not as a 
per cent, but as a fraction of the heat consumed. 

Problem 51i. The steam used for the test cited in Problem 50i was 88 
lbs. per hour, and was at 85 lbs. gage pressure, quality 97 per cent. The 
pump exhaust steam was at 10 lbs. gage. What were the steam consump- 
tion in pounds per horse-power-hour, the heat consumption in B.t.u. per 
horse-power-hour, the thermal efficiency, and the duty? 

Ans,, Eff.=0.86%. 

Problem 5I2. A pump discharges 4750 lbs. of water against a total 
head of 100 ft., in a certain time. During the same time it is supplied with 
100 lbs. of steam and from each pound it consumes 1000 B.t.u. What is 
the duty of the pump? Ans., 4,750,000. 



52. Economy Test of an Injector 

Principles. The injector is a pump in which the heat energy 
of steam is directly used. Works on steam engines and steam 



258 



STEAM PUMP TESTING 



52 



Octaes^ .> Boifer or 
CotfoH' ^ }\Pre66ure 




Injector- 



Feed Wafer Tank--'' 

Fig. 99.— Injector Test. 



boilers describe the instrument in detail. The results from an 
injector test are the same as those from a steam pump test. 

In addition, the number of pounds of 
water pumped per pound of steam sup- 
plied is usually quoted. The methods 
of testing are somewhat different, inas- 
much as a direct measurement of the 
weight of steam per hour is not neces- 
sary, this quantity being obtained from 
the heat balance. 

Fig. 99 shows diagrammatically the 
arrangement of an injector for test. ' 

An expression for the weight of steam 
used per minute is deduced by equating 
the heat energy of the steam entering 
the injector, plus the mechanical and 
heat energy of the water entering, to the heat and mechanical 
energy of the water discharged. The datum of the heat measure- 
ments is at 32° F., and of the energy measurements is the level of 
the injector. 

Let W^ = weights, in pounds per minute; 

/i = heat of the liquid; 

L = heat of vaporization of the steam supplied; 
a: = quahty of the steam supplied, if wet; 
p = pressure of discharge, pounds per square inch; 
Z)',D'' = suction head, and distance between injector 
and gage, feet, respectively; 
/ = temperatures, degrees F. 
Subscripts /, .s. d refer to feed water, steam, and discharge, 
respectively. 

Then, expressing all energies in heat units, and neglecting 
kinetic energy 



WA 



WfD' 



778 



^Ws{hs+xL) = WJia+ 



Wa{2.Sp+D") 
778 



Radiation. 



52 STEAM PUMP TESTING 259 

Also, 

W<i = Wf+Ws. 

Solving these equations simultaneously and neglecting radiation, . 
we have 

hs+xL — hd ^j^ 

In this expression, the heat equivalents of the work are very 
small compared with the other quantities and they may be 
omitted. For the heat of the liquid, /i, in each case may be 
substituted its closely approximate value, t — Z2. There results, 

ts-\-xLd — t 

Selection of the Independent Variable. This may be the 
discharge pressure, the feed water temperature, the suction 
head, or the steam pressure. When the injector is used as an 
ordinary pump, the discharge pressure is perhaps the most 
important of these. If this is selected as the independent vari- 
able, it may be controlled by means of the valve in the discharge 
pipe, see Fig. 99. If the steam pressure is selected, it may be 
varied by the stop valve in the steam pipe, but the gage should 
be placed on the other side of the valve to record the pressure 
on the injector. Whichever quantity is selected, all of the 
others should be kept as constant as possible throughout each 
run, and the injector should be regulated before each run so as 
to secure m.aximum flow. 

(a) Founds of Water Pumped per Pound of Steam. It must 
first be decided whether to credit the injector with the feed 
water only, or with the feed water plus the condensed steam 
which appears in the discharge. If the injector is used for 
emptying J as when draining a mine, the former amount is logically 



260 STEAM PUMP TESTING 52 

used; if for fdlingj as when supplying a tank at a height, the 
latter amount is proper. When used as a boilei feed, there is 
room for some discussion of which is the correct amount. The 
condensed steam is returned to the boiler, but it is used again to 
operate the injector, so strictl}^ speaking it is not a part of the 
useful feed water. On the other hand, a duplex pump used 
for feed water would not return the steam used to drive it and 
would have to pump that much more water. 

From the equation previously deduced, we have 

Ws~ ta-tj ' 

which is the pounds of feed water pumped by one pound of 
steam. Adding one to the numerical value of this expression 
gives the pounds of water plus steam pumped. 

The temperatures are obtained from thermometers appro- 
priately placed in the discharge, feed, and steam pipe; the latent 
heat, from the steam tables; and the quality, from a calorimeter. 
It is often sufficient to assume a value for the quality, provided 
that may be done within 2 per cent of its true value. The 
injector should be run long enough before each run at the required 
conditions to establish uniform temperatures. The run should 
be long enough to secure enough temperature reacUngs for a fair 
average, and for the proper measurement of the quantities 
mentioned later. 

(b) Pounds of Steam per Water Horse-power-hour. The 
equation for Tr«, previously deduced, gives the pounds of steam 
used per minute. The water horse-power is 

^ TT72.3p + /)^ + /)") Tr/D^ + Tr.(2.3p+D") 

^ ^^'t 33,000 ^^ 33,000 

the one or the other to be used according to the considerations 



52 STEAM PUMP TESTING ' 261 

given under (a). The pounds of steam per water horse-power 
hour is then 

^^ 60Tfs 
W.h.p/ 

For this quantity it is necessary to make the same measure- 
ments as enumerated under (a) and also to measure the feed 
water rate and the heads, D' and D'\ The pounds of feed water 
per minute may be determined by any of the methods for measur- 
ing water. A convenient arrangement is to use a hook gage 
or water glass in the tank from which the feed is obtained, by 
which the drop in water level may be timed. This causes a 
variation in the suction head, but if the tank is of generous 
cross-section, the percentage of variation may be small enough 
not to effect the results materially. The average value of the 
suction head may be figured from the readings of water level. 
The head D'^ is, of course, constant throughout the test. 

(c) Thermal Efficiency. When considered merely as a pump, 
the same expression for efficiency as for a steam engine holds, 
l^est 45 (c). 

Efficiency = ^^^^^5^^^^^^^^. 

When considered as a boiler feed apparatus, the efficiency 
is much higher than this because the heat in the discharge is then 
^' useful,'' and the only loss is that due to radiation. A deter- 
mination of radiation may be made from the heat balance if the 
steam supplied is measured as well as the feed water, from which 
the boiler feed eflficiency may be found. This requires much 
more precision in all the test measurements than the other 
results do, however, because the radiation is a small difference 
between two large quantities. 

(d) Duty. See Test 51 (c). 

(e) Capacity should be figured in gallons per twenty-four 



262 BOILER TESTING 53 

hours from the test results of TT/ or TTd, according to the use 
to which the injector is to be put. 

Problem 52:. A test of an injector yields the following data. Steam 
pressure 100 lbs. gage; quality, 97 per cent; temperature of feed, 60° F.; 
temperature of discharge, 147° F.; pressure of discharge. 105 lbs.; gage in 
discharge pipe. 5 ft. above injector; level of feed water, 10 ft. above injector; 
cross-section of supply tank, 7.1 sq. ft.: rate of fall of water in supply tank 
while pumping, 4.12 in. per minute. What is the ratio of water pumped to 
steam used, the pounds of steam per W.h.p.-hour, the efficiency, and the duty? 
Base all results on the total amount of discharge. Ans., EflF. =0.38^. 

Problem 52^. What should be the capacity of an injector to supply a 
100-H.p. boiler, if it oj)erates onl}' two-thirds of the lime? 



53. EcoxoMY Test of the Pcxsometer 

Principles. The pulsometer is a pump in which the pressure 
energy of steam is applied directly to the water pumped without 
intermediate pistons. It consists of two cast-iron chambers 
controlled by automatic valves and working alternately. Steam, 
entering one, discharges the water by its superior pressure, 
while in the other, the partial vacuum, formed from steam con- 
densed by contact with the water, draws a fresh supply of feed. 

The results from a pulsometer test, the equations to be used, 
and the method of testing are exactly the same as for an injector 
test, 52, to which the reader is referred. 

54. EcoxoMY Test of a 5te.\m Boiler 

Principles. The heat available in the coal consumed in the 
furnace of a steam boiler is distributed under four heads: First, 
the useful heat which goes to evaporate the feed water; second, 
the heat lost with the carbon slipping through the grate or 
removed in cleaning: third, the heat carried up the stack by the 
exhaust gases; and fourth, the heat lost by radiation and all 
other\\nse unaccounted for losses. The heat carried up the 
stack may be traced under the subheads, heat carried as tem- 



54 BOILER TESTING 263 

perature of the dry exhaust gases, heat carried by steam formed 
by evaporation of water in the coal and from the combustion of 
hydrogen, and heat lost through incomplete combustion of 
carbon, hydrogen, and hydro-carbons. 

A complete boiler test to determine these quantities includes 
measurements of feed water and coal supplied for a counted time, 
and analyses of the coal, ash, and flue gases. 

Besides the heat balance, certain other quantities are to be 
found for the purpose of comparing the general performance of 
the boiler with that of others. The following terms should be 
understood in this connection. 

A unit of evaporation (U.e.) is 970.4 B.t.u. added to the feed 
water. This unit equals the latent heat of steam at atmospheric 
pressure. A unit of evaporation will therefore make one pound 
of dry steam in a boiler operated at atmospheric pressure and 
supplied with feed water at 212° F., or, more briefly, ^^ from and 
at 212 degrees.^' 

The factor of evaporation (F.e.) is the number of units of 

evaporation added to each pound of the feed water. If H is 

the tetal heat of 1 lb. of steam generated under the existing 

conditions of pressure and quality, and /i' the heat of the feed 

water, both counted from 32 degrees, then the heat added per 

pound is H — h\ and 

// — /?' 
Factor of evaporation * = . 

Equivalent evaporation (E.e.) may be regarded as the number 
of units of evaporation added to a stated amount of feed water, 
and is expressed in units per hour, or per square foot of heating 
surface, or per pound of fuel, etc. Since each pound of feed 
water has F.e. units of evaporation added, 

E.e.* = No. of pounds of feed water X F.e. 

* The boiler code of the A.S.M.E. states that the factor of evaporation 
(for wet steam) is {H — W)-^^10A, in which H is the total heat of saturated 



264 BOILER TESTING 54 

This quantity also equals the number of pounds of dry steam 
which would be generated by the transfer of the same quantity 
of heat in a boiler operating '' from and at 212 degrees/^ Equiv- 
alent evaporation is generally referred to as a number of pounds 
of steam under these conditions. 

A boiler horse-power (Bo.h.p.) is generated when 34.5 units 
of evaporation are transferred to the feed water per hour. Know- 
ing the total number of units of evaporation developed during 
one hour in any boiler trial, the boiler horse-power is 

U.e. per hour 



L.e. per 

^^•^•p-= — 34:5 



The numerator of this fraction is equivalent evaporation per 
hour. Therefore 

^ , Pounds of feed water per hourXF.e. 
Bo.h.p. = 3^;^ — 

If in this expression we put Bo.h.p. = 1, then the pounds of 
feed water per hour equals ^p-^. That is 

The nxLinher of pounds of feed water to he evaporated in one hour 
to mahe one boiler horse-power equals 34.5 divided by the factor 
of evaporation, the latter quantity being fixed by the conditions of 
feed water and steam. 

The rate of combustion for coal-fired furnaces is the number 
of pounds of coal consumed per hour per square foot of grate. 

steam at the boiler pressure. In figuring equivalent evaporation, a '-factor of 
correction" is then applied for quahty, this factor being 1 lb. of moisture 
per pound of mixture. This calculation ignores the heat transferred to the 
water, not evaporated but appearing as wetness. The code, however, gives 
another expression for the "factor of correction" (to be used "if extreme 
accuracy is required") which, when multipUed by the code's expression for 
factor of evaporation, reduces to the same expression for F.e. as defined in 
this work. 



■^i^^^ 



54 BOILER TESTING 265 

Duration of test is governed by the error of starting and stop- 
ping. All the conditions of the boiler and furnace should be the 
same at the end of the test as they were at the beginning, espe- 
cially in regard to the quantity and quality of coal on the grate, 
and water in the boiler. If the coal remaining on the grate at 
the end of the test is greater than that on the grate at the start, 
the furnace will be charged with a greater amount than it has 
actually consumed, and vice versa, unless an estimate is made 
of the difference between the amounts. The probable error of 
such an estimate is greater in the case of the coal than of the 
water. Consequently, the error in the coal measurement deter- 
mines the duration of the test. The test should be long enough 
to make the error of starting and stopping less than 1 or 2 per 
cent of the total amount of coal fired. Assuming this error 
to correspond to a difference of 1 in. in the fuel bed, the result- 
ing error in the coal quantity will be 2.5 lbs. for each square 
foot of grate surface, the weight of a cubic foot of incandescent 
coal being about 30 lbs. Two and one-half pounds is 1 per 
cent of 250 lbs., so the test should be continued until a total 
of 250 lbs. of coal per square foot of grate surface has been £red. 
The higher the rate of combustion, the shorter is the duration. 
If the rate is 20, for example, the test should be about twelve 
hours long. 

In all cases, the length of the test should be a multiple of 
the regular cleaning period in order to cover and keep constant 
regular operating conditions. In the example just cited, if the 
cleaning period is eight hours, the test should be continued for 
sixteen hours. 

Starting and Stopping. The boiler should be operated during 
a preliminary run and complete readings taken until they show 
uniformity of all conditions. The furnace should then be thor- 
oughly cleaned, enough live coal being left on the grate, as in 
usual cleaning, to start a new fire. The thickness of this coal 
bed should be estimated and noted, and the level of the water 



266 BOILER TESTING 54 

in the water column marked with a string tied around the glass. 
The boiler is then fired with a fresh charge of weighed coal, the 
time of firing the first shovelful of which is taken as the start 
of the main test. The ash-pit should then be cleaned and all 
temperatures, pressures, etc., read. At the end of the test, the 
cleaning is repeated in exactly the same way as at the beginning, 
the time of firing the first shovelful of the fresh coal after clean- 
ing being taken as the end of the test. The same observations 
are made as at the beginning. It is best to note the water level 
just after the cleaning, with the fire door open, because then there 
will be a minimum of ebullition to cause a false level. 

Sampling of the coal should be done as for the proximate 
analysis Test 37, page 165. Sampling of the flue gas is described 
under Test 40, page 193. Sampling of the ashes and refuse 
removed in cleaning and falling through the grate is according 
to the sam.e principles as for coal. The steam should be sampled 
for quality determinations, page 144. 

To make clear the quantities resulting from a boiler test, 
a set of calculations from observations made for an actual test 
will be given for each quantity analyzed in the following. The 
condensed or average observations are given below. 

DATA FROM A BOILER TEST AND NOTATION USED IN FORIMULAS 

Duration of test, hours =12 

Total weight of coal as fired, pounds =4925 

Total weight ash and refuse, pounds =734 

Total weight water evaporated, pounds =36,400 

Boiler pressure, pounds per square inch, abs =110 

Quality of steam, x =0. 992 

// = Temperature of feed water, degrees F =98 

/ = temperature boiler room, degi'ces F =80 

Te = temperature flue gas, degrees F =680 

Proximate analysis. Percentages by weight of coal as fired. 

Moisture = 2 . 75 

Volatile matter = 6.00 

Fixed carbon =78.45 

Ash =12.8 



BOILER TESTING 



267 



Weight of carbon in 1 lb. of refuse = . 20 

m, vniy /r = weights of moisture, volatile matter, and 

fixed carbon per pound of dry coal, 

respectively. 
Heat value of coal by calorimeter = 13,040 

Volume Analysis of the Flue Gas, Per Cents 

£) = carbon dioxide =11.0 

O =oxygen = 9.0 

M = carbon monoxide = 0.5 

iV = nitrogen =79.5 

Weights, in Pounds, of Carbon from 1 lb. of Dry Coal 

Ca — carbon wasted in ash ; 

Ci= total carbon; fixed, and in volatile matter; 

C^ = carbon burned, appearing in flue gas. 

(a) Determination of Total Coal and Refuse. The coal to be 
fired is weighed out by the barrowful as it is needed and heaped 
on the boiler room floor at a place convenient for firing, one 
barrowful at a time. The following is the best form of log for 
coal records. It includes a few observations to illustrate its 
purpose. 



Weight of Barrow. 


Net Weight. 


Total Weight. 


Time of Firing 


Empty. 


Full. 


First Shovelful. 


Test started. . 








SrOO A.M. 


100 
100 
100 

Etc. 


250 
275 
260 


150 
175 
160 


150 
325 

485 


8:00 
8:24 
8:16 



A chart should be plotted as the test proceeds of total coal 
as shown by the fourth column against time as a base. It should 
be noted particularly that the time to be plotted against the total 
weight from each barrowful is not the time of firing the first 



268 



BOILER TESTING 



54 



shovelful from the corresponding weighing of coal, because 
this coal is not entirely burned until the first shovelful of the 
next charge is fired. Referring to the log, 150 lbs. should there- 
fore be plotted against 8:24; 325 lbs. against 8: 46; and so forth. 
If the rate of evaporation and all other conditions external 
to the furnace are uniform, then T\'ith proper firing, the rate of 
combustion will be uniform, and a fair straight line will be repre- 
sented b}^ the points of the plot. This line should pass through 
the origin; if it intersects the axis of coal weights above the time 
axis, it indicates that there was too much coal on the grates at 
the start ; if below, too little. In such a case, it is better to figure 
the total coal from the slant of the fine. 

The ashes accumulating under the grates and the refuse 
removed during cleanings in the main test should be collected, 
allowed to cool without wetting, and then weighed. 

(b) Determination of Total Feed Water Evaporated. The 
feed water may be measured by a meter in the feed water line 
but when certainty of accurate results is desired, a direct weigh- 
ing sj'stem such as represented diagrammatically by Fig. 100 
should be used. With this arrangement, the levels of the water 
at the start of the test is marked b}^ the gage, g, in the suction 

tank and by the string on the 
water column at m. The feed 
pump should be operated at 
a constant rate through the 
test, this rate being determined 
by the horse-power required 
of the boiler; and, with proper 
firing and regulation, the water 
level shown by the column 
should always be approxi- 
mately at m. The best form 
of log for the records is as 
follows. A few sample observations are included to illustrate. 



Feed yVafer- 




Fig. 100. — Weighing System. 



54 



BOILER TESTING 



269 





Weight of Barrel. 


Net Weight. 


Total Weight. 


Time of Pass- 


Barrel No. 


Empty. 
Lbs. 


Full. 
Lbs. 


ing Gage 
Level. 


Test starte 


d 








8:00 a.m. 


1 
2 

1 
Etc. 


50 

60 
75 


300 
320 
300 


250 
260 
225 


250 
510 
735 


8:12 
8:25 
8:34 



As the test proceeds, a chart should be plotted of total water as 
shown by the fifth column against the time taken to evaporate 
it as a base. When the first charge, 250 lbs. on the log, is turned 
into the suction tank, the level is raised above the gage, g, Fig. 
100. When the level has again descended to the gage, all of 
the 250 lbs. has then been evaporated provided that none of 
it has accumulated in the boiler as would be show^n by a 
higher level in the column than m. The time of passing 
the gage level in the suction tank is therefore the time to 
be plotted; 250 lbs. against 8:12; 510 lbs. against 8:25; and 
so forth. 

It is especially important to keep the rate of evaporation 
uniform for a valid test. The water-time curve should there- 
fore be a straight line. 

If the water level is not the same at the end as at the begin- 
ning of the test, the total water may be figured from the slant of 
the line, or a correction may be applied to the last figure in the 
fifth column of the log. The correction is calculated from the 
cubical contents of the boiler betw^een the two levels and the 
density of the water at the existing temperature. It should be 
noted that a false level may appear in the water column if the 
ebullition is violent or if the water column is blown dowai within 
a short time before reading. The latter occurrence is due to 
the fact that blowing down forces into the glass hotter and less 
dense water than is there normally. 



'^^ 



270 BOILER TESTING 54 

(c) Quantities to be Found Prior to Calculations of Results. 
The proximate anal^^sis of the coal is generaUy expressed in per- 
centage by weight of the coal ^^ as fired/^ that is, including mois- 
ture. To find the weights per pound of dry coal, it is necessary 
only to divide each of the items by 100 minus the percentage 
of moisture. Thus, for the data of the test previously cited, 

m = 2.75- (100-2.75) =0.0283 lb. of moisture; 
vm = O.GQn lb. of volatile matter; 
/c = 0.807 lb. of fixed carbon; 
a = 0.132 lb. of ash; 
vm+fc = 0.86d lb. of combustible. 

It is necessary to know the total carbon per pound of dry 
coal. If the ultimate analysis has been made, this figure is 
available; otherwise, it is necessary to estimate it. The method 
quoted under Test 37 (b) may be used, if the proximate analysis 
only has been made. 

On page 169, the data of the above analysis are used as an 
example of this method, and it was found that the total weight of 
carbon in 1 lb. of dry coal is 

G = 0.807+0.01X0.869 = 0.816 lb. 

The proportion of carbon which is wasted through cleaning 
and grate, Cay may be found in two ways. The first method is 
as follows. 

The total carbon in the refuse equals the total amount of 
refuse minus the ash from the total coal fired. The ash from the 
total coal fired equals the total quantity of coal times the pro- 
portion of ash in it as given by the proximate analysis. Then, 

__ Total refuse, lbs. — Total coal, lbs. X Per cent ash -^ 100 
Total coal, lbs.X(l — Per cent moisture in coal -^100)' 

the denominator being the total weight of dry coal. 



54 BOILER TESTING 271 

The second method uses the proximate analysis of the ash. 
Total refuse, lbs. X Weight of C in 1 lb. refuse 



Cc 



Total coal, lbs.X(l — Per cent moisture in coal -^ 100) 



In the first equation it is assumed that all of the ash coming from 
the coal fired during the main test is removed with the refuse. 
This, however, is uncertain, so it is better to use the second 
method. Applying the data of the test under consideration, 
each pound of the refuse was found to contain 0.20 lb. of carbon. 
The total coal as fired was 4925 lbs. and it contained 2.75 per 
cent of moisture. The total weight of refuse was 734 lbs. Then 

734X0.20 _ 030^ lb 
^^ ~ 4925 - .0275 X4925 ~ -""^"^ ^''• 

To find the weight of the carbon burned. 

For given data C, = 0.816 -0.0307 = 0.785. 

To calculate the factor of evaporation, the heat content of 
the steam generated is first found. Referring to the test data, 
page 266, the steam tables give i? = 305.5+0.992X882.5 = 1181. 
Consequently 

1181-(98-32) _ 
^•^•" 970.4 "^•^^• 

All the items of the heat balance will be figured on the basis 
of 1 lb. of dry coal. The heat value of the dry coal as found by 
calorimeter or calculation (see Test 38) will therefore be the heat 
supplied. 

(d) Equivalent Evaporation, per Pound of Coal as Fired, is 

^ _ Total water evaporated, Ibs.XF.e. 
Total coal as fired, lbs. 



272 BOILER TESTING 64 

The units of this expression are either pounds of water evapo- 
rated from and at 212 degrees per pound of coal, or units of evapo- 
ration per pound of coal. For the given data (page 266), 

^ 36400X1.15 ^^,, ^, 

E.e.c. = -rz^rz = 8.5 lbs. or U.e. 

492o 

Per pound of dry coal 

E.e.d.c. = E.e.c. ^ (1 — moisture, lbs.), 

For the given data, E.e.d.c. = 8.5 -^ (1 - .0275) =8.65 lbs. or U.e. 
Per pound of combustible 

E.e.cb. = E.e.d.c. -^ {vm+fc), 

1^ or the given data, E.e.cb. = 8.65 -^ 0.869 = 9. 95 lbs. or U.e. per hr. 

Per hour 

_, , Total water evaporated, lbs. xF.e. 
E.e.hr-= 



'1 otal time, hours. 
For the given data, 

E.e.hr. = (36400Xl.l5)--12 = 3440 1bs. orU.e. perhr. 

(e) Over-all Efficiency. Since there are E.e.d.c. X 970.4 B.t.u. 
added to the fc^ed water for each pound of dry coal fired, and since 
the heat available from this coal is its heat value, the efficiency 
is, 

E.e.d.c. X97 0.4 

Heat value of dry coal* 

For the given data, over-all efficiency = 8. 65X970.4^13,040 = 65 
per cent. 

(f) Loss to Carbon Wasted in Refuse. Taking the heat 
value of carVjon as 14,600 B.t.u., this loss per pound of dry coal is 

14,600Ca. 



54 BOILER TESTING 273 

For the given data, 14,600X0.0307 = 448 B.t.u., or 448-^ 13,040 = 
3.4 per cent. 

(g) Loss of Heat to Dry Exhaust Gases. This determination 
involves the measurement of the excess of temperature of the 
flue gas over that of the boiler room, and of the weight of 
dry flue gas per pound of dry coal, TF^. For the specific heat, 
an average value, 0.24, may be used with sufficient accuracy. 
Then the loss is 

0.24XTF,X(r.-0. 

To find Wd the formula given on page 199 may be used. For 
the given data 

Wd = — — 11 ci'in K h. 785 = 17.3 lbs. per lb. of dry coal 

1 l.u~r"U.o 

and the loss is 0.24X 17.3 X (680-80) =2490 B.t.u. or 2490-^ 
13,040 = 19.1 per cent. 

(h) Loss of Heat to Water Vapor in the Flue Gases. To calcu- 
late this, we must know the weight of vapor per pound of dry coal 
and its heat content above room temperature, including latent heat. 
The vapor carried in as humidity of the air need not be considered 
because it is small in quantity and its latent heat is not added by 
the coal. This leaves only the vapor from the moisture in the coal 
and that due to combustion of hydrogen to consider. From the 
formulas for Wv, the weight of vapor per pound of coal, on page 
200, and for the heat of steam w^hen mixed with flue gases on 
page 143, we have 

Loss per pound dry coal = (9i:/r+7n) (1090+0.46^^-0. 

Ht, the weight of hydrogen per pound of dry coal, may be deter- 
mined according to Test 37 (6) in the case of semi-anthracite 
and bituminous coals if the ultimate analysis has not been made. 
For the proximate analysis of the given test, the calculation for 
Ht is made on p. 169, resulting in ^^2 = 0.025. Therefore the heat 



274 BOILER TESTING 54 

lost is (9X0.025+0.0275) (1090+0.46X680-80) =335 B.t.u. or 
335^13,040 = 2.6 per cent. 

(i) Loss of Heat Due to Incomplete Combustion. Considering 
only the incomplete combustion of carbon, the loss of heat when 
1 lb. of carbon burns to CO instead of COo is 14,600-4400 = 10,200 
B.t.u. (seepage 169). In the boiler test there are TT^ lbs. of carbon 
per pound of dry coal burned to CO. An expression for Wi 
is derived on page 200. The loss is 

10,200 Xir. B.t.u. per pound of dry coal. 

For the given data, 

Heat lost = 10.200 X ^':y,^;/,^'^ = 338 B.t.u. or 338-13,040 

11-rO.o 

= 2.7 per cent. 

(j) Radiation is found by difference. For the given data, it is 

100^c-65rc-3.4%-19.1%-2.6rc-2.7rc=7.2% 

(kj Other Quantities. The boiler horse-power is, as previously 
defined, 

1^ = 99.9 B.h.p. 
34.0 

The equivalent evaporation per hour per square foot of heat- 
ing surface is, 

E.e.hr. 
Sq.ft. of surface* 

For the given boiler, the heating surface was 1000 sq. ft., so 
E.e.hr. per square foot = 3440-^1000 = 3.44 lbs. or U.e. 

The grate surface of this boiler was 30 sq. ft., so the rate 
of combustion of dr\" coal, as previously defined, was 3994-30 
= 13.3 lbs. per hour per square foot. 



54 BOILER TESTING 275 

Efficiency of the Grate and Cleaning. The proportion of the 
combustible lost is Ca-^ (vm+fc). Consequently this efficiency is, 

Ca 



vm+fc 



For the given data, this is 1 - 0.0307 -^ 0.869 = 96.5 per cent. 

Efficiency of the boiler and furnace (exclusive of grate) is 
the over-all efficiency divided by the efficiency of the grate. For 
the given data, this is 65-7-96.5 = 67.4 per cent. 

This efficiency is often defined as the heat absorbed per pound 
of the combustible burned divided by the heat value per pound 
of combustible. 

The excess coefficient may he found from the expression 
derived on page 201. 

Besides the total water and coal curves, it is well to plot, 
after the test, all the readings of pressure, feed water, flue and 
boiler room temperatures, per cent CO2 and the draft in inches 
of water. These will be broken curves. They will aid deduc- 
tions of causes of any irregularities in the performance. 

A few barometer readings are desirable in connection with 
natural draft. 

All circumstances that may affect the conditions of the test 
should be carefully noted for possible future reference. 

Problem 54i. A 50-H.p. boiler delivers steam at 175 lbs gage, super- 
heated 100°, from feed water at 50°. What is the F.e.? How many pounds 
of feed water will be needed per hour during a test? Assuming an efficiency 
of 70 per cent and anthracite coal with 15 per cent ash, about how many 
pounds of coal will be needed per hour? Ans.y 1.27; 1360 and 190 lbs. 

Problem 642. For a given natural draft, there is a corresponding flue 
temperature necessary to maintain it. If the excess air during the opera- 
tion of a boiler varies, and all other conditions remain constant, deduce the 
relation between per cent CO2 and efficiency. Note that efficiency = 1— a 
constant— loss to dry exhaust gases, approximately. 



276 TESTING OF STEAM AUXILIARIES 55 

55. Test of a Surface Condenser. 

Principles. A steam condenser receives, in practice, a mix- 
ture of steam and water and air. The steam entering the con- 
denser, if exhausted from a steam engine or turbine, carries with it 
moisture. Air enters the system through leaks in steam-pipe 
joints, stuffing boxes, and from the boiler feed. 

Since it is the function of a condenser (considered as a power 
unit) to maintain a vacuum, this is one of the most important 
items to mvestigate. Under ideal conditions of heat transfer, 
the vacuum possible to be maintained would be that of saturated 
steam corresponding to the temperature of the outgoing con- 
denser water. This ideal is not realized for two reasons. First, 
a difference of temperature between the steam and the cooling 
water is required that there should be a heat flow from the one 
to the other. Second, the effect of air mixed with the steam is to 
make a higher pressure than that due to the steam alone, accord- 
ing to the law of partial pressures (see p. 142). If, for example, 
the temperature in the steam space of a condenser were 126° F. 
the corresponding steam pressure (from the tables, p. 370) is 
2 lbs. absolute, ver}^ nearly. Suppose there is air present, in amount 
equal to one-quarter by weight, of the steam. A cubic foot of 
the steam space would then contain a weight of air equal to one- 
quarter of the density of steam at 2 lbs., absolute, and the specific 
volume of the air would be four times that of the steam, that is, 
4X174 = 696 cu.ft. per pound. Consequently (from PV = RT), 

^ ..I • 53.4 X (126+460) ^^ „ . , 

Pressure of the an- = ^ . , ^,nr^,^ ^ = .31 lb. per square mch 

144Xbyo 

and the pressure of steam and air combined woukl be 2+. 31 = 2.31 
as compared with 2 lbs. if the steam space contained steam alone. 
It follows, then, that the effect of air upon condenser performance 
is to increase the absolute pressure above that corresponding to 



55 TESTING OF STEAM AUXILIARIES 277 

the prevailing temperature, and therefore to lessen the effective- 
ness of the condenser. 

The question of the most economical vacuum is a pertinent 
one in connection with condenser tests. This leads to a consid- 
eration of the cost of cooling water, and of auxiliary power, that 
is, of circulating, wet air, and dry-air pumps. 

Finally, the rate of heat transmission should be investigated 
in order to determine the effectiveness of the cooling surface. 

The Independent Variable may be the vacuum, weight of con- 
densate, or the quantity of cooling water per unit of time. 

The following notation will be used in this and the next test. 

TF^^== weight of cooling water, pounds per hour; 
T7s = weight of w^et steam entering, pounds per hour; 
Wr = weight of cooling water per pound of condensate; 
Ts = temperature of the steam in the condenser, degrees F.; 
^s = temperature of the condensate discharged; 
Ti = temperature of cooling water at inlet, degrees F.; 
To = temperature of cooling water at outlet, degrees F. ; 
T';n = mean temperature difference betw^een steam space and 
cooling water, degrees F. ; 
Xj L = the quality and latent heat of the entering steam ; 
5 = heat transmitted, B.t.u. per hour; 
A = area cooling surface, square feet. 

(a) Ideal and Actual Vacuums. The actual vacuum may be 
measured with a calibrated gage, its indications being reduced 
to absolute pressure by subtracting them from the barometric 
pressure as observed. Or, better yet, an '' absolute pressure 
gage '^ may be used. This may be in the form of a glass U-tube 
with one leg sealed at the top and completely filled with mercury. 
A sufficient reduction of pressure on the open leg will lower the 
mercury column in the filled one; the difference of level in the two 
legs of the U-tube then is the absolute pressure. A heavy rubber 
tube, capable of withstanding 15 lb. collapsing pressure, may be 



278 TESTING OF STEAM AUXILIARIES 55 

used to connect the open leg of the U-tube to the condenser steam 
space. The steam inlet pipe should be tapped, close to the con- 
denser, for a |-inch pipe nipple. Another opening should be 
made for the insertion of a thermometer. 

The condenser should now be operated^ as in regular ser- 
vice, at a predetermined vacuum, for a period of say one-half hour. 
During this time, at intervals of five minutes, temperature readings 
should be taken of the steam and of the discharge from the wet 
air pump or hot well pump, the vacuum being maintained con- 
stant. If there is but little air in the steam, and the pressure 
drop through the condenser is small, the absolute pressure as 
shown by the gage should be but shghtly greater than that of 
saturated steam corresponding to the average temperature of the 
steam space or of the discharged condensate. A large quantity 
of air leakage, on the other hand, will be indicated by a material 
difference between these pressure values. 

A series of such tests may be run at various values of the 
vacuum. It is useful to plot the resulting data, actual against 
ideal vacuum (corresponding to both Ts and ts)^ for the purpose 
of later comparisons. 

(b) Rate of Heat Transmission. Since the quality of the 
incoming steam is generally difficult to measure (because it con- 
tains a large amount of moisture), the heat transmitted is best 
determined by finding the heat added to the cooling water. The 
water quantities are usually large, and therefore some form of 
velocity meter is appropriate for measuring the water supplied. 
Inlet and outlet temperatures of the cooling water (close to the 
condenser) must be read and averaged. From these data (see 
notation, p. 277), may be calcvlated the heat transferred per hour. 

B = W^{To-Ti), 

(c) EiBfectiveness of Heat Transmission. This can be judged 
after determining the number of B.t.u. transmitted per square 



55 TESTING OF STEAM AUXILIARIES 279 

foot of surface per hour per degree difference in temperature. 
This result represents the conductivity of the heat path, and will 
be referred to as C. Then 

c " 



The mean temperature difference, Tmj is found from the relation 

To-Ti 



J- m — 



log. 



'" Ts 



which is deduced in treatises on heat transmission. Substituting 
this value and the one previously quoted for B in the equation for 
C, we have 

The value of C resulting from this equation should be about 
300 B.t.u. for ordinary installations, and, in the best designs, as 
high as 900 B.t.u. Low values indicate fouled surfaces, air pock- 
eting, flooding, etc. 

It may be noted from an examination of the equation for 
C that the more nearly equal are Ts and To, the more effective 
is the heat transmission. These temperatures, by themselves, 
are therefore a criterion of performance. 

Another statement of the effectiveness of heat transmission is 
in terms of weight of condensate per square foot per hour. This 
is not very definite, since it depends upon the latent heat of the 
steam and consequently the vacuum, as well as the quahiy of the 
steam. Ordinarily it is about 10 lbs. 

(d) Weight of Condensing Water per Pound of Condensate. 
Under ideal conditions, with dry steam, this would be 

, L 



280 TESTING OF STEAM AUXILIARIES 56 

Actually it is 

_ xL + {Ts-ts) 

plus an amount necessary for cooling the entrained air, radiation, 
etc. The value of uv may be calculated from this equation, pro- 
vided an estimate of x is made, and compared with the ratio of 
weights of cooling water to condensate as obtained by metering 
both. 

(e) Leakage Tests of surface condensers may be made accord- 
ing to the directions on page 231. 

Problem 55i. The gage on a condenser shows 3.45 ins., absolute. The 
temperature of the steam space is 115°. What percentage of air is present 
(based on the mixture)? An^., 20%. 

Problem 552. A condenser operating at 26 ins. vacuum (norma^ barometer) 
takes cooling water at 60° and discharges it at 116°. What is the mean tem- 
perature difference? yln.s., 29.7°. 

Problem 553. If in the preceding, 200,000 lbs. of cooling water are used 
per hour, and the area of the cooling surface is 1000 sq.ft., what is the value 
of C? Ans., 377B.t.u. 

Problem 55.1. Using data of Problem 552, how many pounds of cooling 
water are required per pound of condensate, assuming dry steam and allowing 
12% for heating air, radiation, etc.? ^ns., 20.5 lbs. 

56. Test of a Jet Condenser 

Principles. These are, in the main, the same as for the pre- 
ceding, Test 55. There is this difference, however, that, since 
condensate and coohng water are mixed, the outlet temperature 
of the latter. To, equals that of the former, U. 

(a) Ideal and Actual Vacuums. See Test 55 {a) 

(b) Rate of Heat Transmission. The method of Test 55 (6) 
may be used with the modified formula. 

If the weight of the discharge from the condenser is measured 
instead of the inlet water, TF^, then steam entering the condenser 



57 TESTING OF STEAM AUXILIARIES 281 

must be separately determined and subtracted from the total 
weight to find JVw 

(c) Weight of Condensing Water per Pound Condensate See 
Test 55 (d). In the formulas quoted ts maybe substituted for 
To since the two are the same. 

Problem 56i. A jet condenser operates under a vacuum of 26 ins. and takes 
condensing water at 70° F. Assuming the steam dry, and containing no air, 
how much water is required per pound condensate under ideal conditions? 

Ans., 18.2 lbs. 

Problem 662. A jet condenser operates under a vacuum of 26 ins. and 
takes condenser w^ater at 70° F. The temperature of the wet air pump 
discharge is 10° below that of the steam. Allowing 10 per cent for cooling the 
air, etc., how much water is required per pound of condensate fromdry steam? 
(Compare with 56i). Ans.j 24.7 lbs. 



57. Test of a Feed-water Heater 

Principles. As far as heat transmission is concerned, a closed 
feed-water heater is identical to a surface condenser; and an open 
heater to a jet condenser. Tests 55 and 56 should therefore 
bj read in this connection. 

The closed feed-water heater generally operates with the 
water space under pressure, but the open heater runs practically 
at atmosphere. The steam supplied may be engine or auxiliary 
exhaust. There may be more steam available than can be used 
for preheating the water, in which case the excess is either vented 
to the atmosphere or used in some other apparatus, such as radi- 
ators for room heating. 

There are so many different combinations for the employment 
of feed-water heaters that it is impracticable to state a general 
method of testing covering them all. 

The notation on page 277 will be used, in which, for ^^ cooling 
water " should be understood '^ feed water,'^ and for '^ condenser '' 
^^ feed-water heater.'' 



282 TESTING OF STEAM AUXILIARIES 57 

(a) Useful Heat Transmitted. For a closed heater this is, in 
B.t.u. per hour. 

For an open heater, and for a closed one in which the con- 
densate is returned to the boiler, there should be added to this the 
heat regained in the condensate. 

The quantities in the equation just quoted are to be measured 
as under Test 55 (6). 

(b) Effectiveness of Heat Transmission. For a closed heater 
Test 55 (c) applies. In either type, the more closely does the 
outlet temperature of the water approach that of the steam, the 
more effective is the heat transmission. 

(c) Available Heat. It is useful, sometimes, to estimate the 
heat available in the total steam supplied the heater (above feed- 
water temperature) in order to form an idea of the proportion of 
it that is utilized. As a rule this cannot be determined accurately. 



58. Testing the Adjustment of an Internal CoMBrsTiON 

Engine 

Principles. Most of the modern internal combustion engines 
work on tlie Otto cycle which takes four strokes for a complete 
series of events. First, the suction stroke, in which the piston, 
advancing from the head end, takes in a charge of gas or vapor 
fuel mixed with air. Second, the compression stroke, returning, 
in which the charge is compressed. Third, the expansion stroke, 
at the beginning of which the mixture is burned and afterward 
performs the useful work. Fourth, the exhaust stroke, during 
which the ])urned gases are discharged. Fig. 101 shows this cycle 
of operation on a PV diagram. There are two valves to control 
the charge, one for inlet and one for exhaust. Fig. 102 shows 
where these valves open and close relative to the crank posi- 
tion and on the indicator diagram. It is seen that the inlet 



58 



GAS ENGINE TESTING 



283 



valve opens a little after dead center. This is arranged so that 
it will open after the exhaust valve has closed; otherwise there 
would be a tendency for the 
exhaust gases to enter the in- 
take. The closing of the inlet 
valve takes place after crank 
end dead center so as to pro- 
vide a good opening for the 
charge. The corresponding 
crank angle may be as much 
as 20° to 30°, with high-speed 
engines; the momentum of the 
incoming gases causes them 

to continue to flow into the C3^1inder during the inward piston 
motion. The exhaust valve should open a little before crank end 




Suction 

Fig. 101.— Otto Cycle. 





^ 



o^^ f cr-^i o 



^v. ^^ ^^, ^^ 

Inlet Opens. inlet Closes. Exhaust Opens. EAhwus-t Closes. 

Fig. 102.— Gas Engine Valve Events. 



dead center and close a little after the opposite dead center to 
allow free egress of the burned gases, the amount depending upon 
the speed and type of the engine. The correct angular distances 
of the crank from the dead center positions, corresponding to the 
valve events, are usually stated by the engine manufacturer. 

Ignition of the charge should occur in the neighborhood of 
dead center; generally before, when the engine is running. This 



284 



GAS ENGINE TESTING 



58 



is because it takes an appreciable time for the gas mLxture to rise 
to its maximum pressure after ignition. For maximum power, 
the greatest pressure should occur at the beginning of the stroke; 
consequently, ignition should ^' advance '^ this position. The 
greater the rotative speed, the greater will be the angular dis- 
tance, or advance, between the crank and dead center when 
ignition takes place. Some fuels burn more slowly than others; 
for such the ignition must be more advanced. The angular 
distance varies between zero and 50°. 

(a) Timing the Valves. This is done by reference to the crank 
positions when the valves are opening or closing. A prick point 
should be made on the fl^-wheel rim to mark the line of the crank, 
and the position of this prick point located by trammels or other- 
wise when the engine is on dead center. The angular distance 
between the prick point and its dead center position will deter- 
mine the motion of the crank for any valve event. 

The valves usually are operated by cams on a cam shaft 
driven by 2 to 1 gears, a and b, from the main shaft. See Fig. 

103. There is a certain amount of clearance 
^ y-vyf ye between the valve stem and the cam when 

^ 1 I ^ ^ the latter is not acting. By changing this 

clearance the timing of the valve will be 
altered. From the figure it will be seen 
that to make the clearance greater makes 
the valve open later and close earlier. The 
timing may be changed also by changing 
tl.e relative positions of the gears a and 
b. Thus, in the figure, if gear a is turned 
lack (clockwise) so that it meshes with one 
tooth behind on 6, both opening and closing 
will be later. 

There is usually some pro^'ision made for changing the clear- 
ance. The Drocedure in timing the valves, then, is first to locate 
the crank positions corresix)nding to oj^ening and closing, and then 




Cears- y. 



Fig. 103. 
Gas Engine Valve. 



58 GAS ,ENGINE TESTING 285 

to correct, if necessary, by changing the clearance or gear mesh 
or both. The point of opening or closing may be accurately 
fixed by turning the valve stem with the fingers; the friction of 
the valve when seated is easily felt. It should be noted that the 
valve events are somewhat different when running because of 
the expansion of the valve stems due to the working tempera- 
ture. To allow for this, the engine may be operated until it 
warms up, and then timed. The makers' instructions for timing 
are usually for the cold condition. 

With high-speed engines, such as are used in automobile and 
marine practice, it is customary to set the valves by making 
each clearance a stated amount, and this amount is usually very 
small, between 0.002 and 0.006 in. The purpose is to minimize 
the noise and wear which are produced by excessive clearance. 
Clearances are often made on such engines as small as the mechanic 
can make them. Systematic procedure calls for the use of ^^spacer^' 
gages, or '' feelers,'' by the use of which the clearances may be 
made exact. After such adjustment, the valves should be timed. 
It is more important to get good timing on exhaust than on 
inlet valves. 

(b) Timing the Ignition. For jump spark ignition with 
batteries or low-tension magneto, this is readily done by remov- 
ing the spark plug and noting the crank position to correspond 
with the occurrence of the spark. For high-tension magneto 
systems, the timer on the magneto must be observed. For 
make-and-break systems, it is easy to note the crank position 
when the igniter breaks contact, as it is visible. 

For economical running, ignition should be advanced as 
far as possible without causing pounding or diminution in speed. 

(c) Adjustment of Mixture. Whether the engine uses oil 
vapor or fuel gas, there is one device for setting the amount of 
air supplied and another, the amount of fuel. Strictly speaking 
these should be readjusted for every load on the engine, but 
usually a single adjustment is made to give the best mixture at 



rrr 



286 GAS ENGINE TESTING 58 

usual running loads. As a general rule, it may be accepted that 
the mcst economical mixture is as dilute a one as may be had 
without causing misfiring or objectionable slowing dowTi of the 
engine. This effect is due to the lower working temperatures of 
the expanding medium. Also, for economy, the fuel valve should 
be open as little as possible. This is especially the case with 
engines with throttling governors. If the engine is given too much 
fuel, it tends to speed up w^hich puts upon the governor the work 
of throtthng it so that the suction in the C3dinder is greater and the 
line 1-2, Fig. 101, is lower. Thus the greater the throttling, the 
larger will be the lower loop of the indicator diagram. This 
represents the work lost in pumping the charge into the cylinder. 

AVith an engine regulated b}^ a governor, the procedure is 
as follows. The desired load is applied by brake or otherwise 
and the valve controlling the flow^ of fuel is set with a slightly 
larger opening than is thought to be correct. The air opening 
is then increased until the engine shows signs of slowing do\\Ti, 
as determined by a tachometer. Records of speed and valve 
settings for this trial are kept. The procedure is then repeated 
with a slightl}' less fuel valve opening. The smallest fuel valve 
opening with the largest air valve opening which will not cause 
objectionable slowing down or irregular firing may be accepted 
as the best setting for the applied load. In this connection 
it is essential that the exhaust be observed during each trial; 
it should be clear and regular. 

(d) Adjustment of Carburetors for variable speed engines 
supplied with gasoline, such as automobile and marine engines, 
is more difficult than the adjustment of mixing valves on constant 
speed engines, but the same principles are to be observed. ]\Iany 
carburetors are made with automatic adjustment to accommodate 
changes of speed, and the adjustment is made with the engine 
delivering no torque. This procedure is convenient, but not 
productive of best results. In general, it is a good plan to follow 
the manufacturer's instructions for carburetor adjustment to 



58 GAS ENGINE TESTING 287 

get what may be considered an approximate setting. A read- 
justment then should be made, under a load representing the 
average running condition. This readjustment involves reducing 
the needle valve opening and increasing the auxiliary air opening 
to a point just short of back firing. This will give the most 
economical^ although not the most "powerful^ mixture. Also, it 
will probably be necessary to determine another setting for starting 
the engine when cold. 

Finally, the action of the carburetor should be judged by the 
appearance and sound of the exhaust. 

(e) Test of Timing by Indicator. This applies to engines 
running at not more then 250 R.p.m. if the ordinary indicator 
is to be used. Special gas engine indicators are made to handle 
about double this speed. Higher than this, only optical indi- 
cators may be used with success. A light spring should be used 
in the indicator, about 20 lbs., and the indicator piston arranged 
with a stop so that it will not register much above atmospheric 
pressure, in order to get the suction diagram on a larger scale. 

If the inlet valve opens too late, the line from 1, Fig. 101, will 
not have as sharp a drop as it should and the suction line wall 
be lower. If the inlet valve closes too late, the compression 
curve will not start sharply from the point 2. If the exhaust 
valve opens too late, expansion is carried a little beyond point 
5, but the beginning of the exhaust line will be higher on account 
of the greater back pressure. If it closes too late, the effect is 
much the sam_e as for too late opening of the inlet. When the 
valve events are too earh, opposite effects will be recorded. 

There is an important connection between the timing of the 
exhaust valve and economy in the use of fuel. This has to do 
with the ^^ scavenging ^^ of the cylinders, that is, the cleaning out 
of the exhaust gases, which is necessary to the complete com- 
bustion of the next charge. Hence the exhaust valve should be 
kept open for as long a crank motion as other conditions permit. 

The indicator diagram does not show fine differences in the 



288 GAS ENGINE TESTING 58 

timing of the valves because the events occur near the ends of 
the stroke where the indicator drum has but little motion corre- 
sponding to the angular motion of the crank. For this reason, 
it is useful to set the reducing motion of the indicator 90 degrees 
ahead of the crank, so that the valve events will be shown in the 
middle of the indicator diagram. 

If the ignition is properly advanced, the line 3-4, Fig. 101, 
will be vertical. If ignition is too late, this line will slant as 
shown by the dotted line 3-4', causing a diminution of power; 
if too early it will slant in the opposite direction with the same 
effect, accompanied by pounding. 

Problem 58i. An inlet valve is found to open too early and close too 
late. The exhaust valve on the same cjdinder opens and closes too early. 
What should be done to correct the timing, if the two cams are integral 
with the cam shaft? 

Problem 582. Draw two indicator diagrams, each superposed on a normal 
diagram like Fig. 101, to show the effects of too early and too late valve 
events. 

Problem 683. Draw a suction diagram to be expected with normal set- 
ting when the reducing motion is set 90° ahead of the crank. Draw the 
work diagram. 

59. Mechanical Efficiency Test of an Internal 
Combustion Engine 

Principles. Exactly the same methods and formulas apply 
to this test as to Test 44, \vith the exception of the determina- 
tion of iV in the formula for indicated horse-power. Internal 
combustion engines are generally single acting in moderate sizes, 
so, with throttUng governors and regular firing, there is only one 
power stroke for each two revolutions of a crank. Under these 
conditions, the value of A^ is one-half the revolutions per minute. 
When the engine governs on the hit-and-miss principle, how- 
ever, the actual number of explosions per m.inute must be 
counted. This also applies with a throttling engine if the firing 
is irregular. 



69 GAS ENGINE TESTING 289 

The indicator diagram, Fig. 101, contains a negative area 
which must be subtracted from the upper area to get the net 
mean effective pressure. This may be done with the planimeter 
by traversing the upper area in a clockwise direction, and the 
lower, anti-clockwise. The indicated horse-power obtained from 
the result is the '^ net '^ I.h.p. which is greater than the brake 
horse-power by the horse -power given to mechanical friction. 
The lower loop of the diagram gives the work lost to fluid fric- 
tion, that is, to pumping the charge into the cylinder. It may 
be determined accurately only by using a light indicator spring 
as explained under Test 58 ie) . 

(a) Determination of Indicated Horse-power. See Te^t 44 
(a). If the engine governs on the hit-and-miss principle^ the 
explosions may be counted by timing the sound of the exhaust 
if the speed is not too fast. Special devices are made for this 
purpose when a continuous record is wanted. One may be 
made by tapping a small pipe into the exhaust and covering 
it with a flap held down by a spring. An explosion causes the 
flap to rise and so actuate the lever of a revolution counter. 

(b) Friction Horse-power. The mechanical friction is obtained 
as for Test 44 (6) . The fluid friction may be expressed as horse- 
power calculated from the mean-effective pressure of the lower 
loop, the value of N being the same as for the net I.h.p. 

(c) Efficiency, (d) Speed Regulation. See Test 44 (c) and (d). 

Problem 59i. A 2-cylinder, 6-in.X8-in.X350 R.p.m. gas engine, govern- 
ing on the hit-and-miss principle, misses one out of every five explosion 
strokes. If the net mean-effective pressure is 20 and 21 lbs. in the two 
cyhnders, what is the I.h.p.? Ans.y 3.28 H.p. 

Problem 592. What is the engine constant of a 6-in.X8-in. gas engine? 
If the brake horse-power is 5, and the M.e.p. of the upper loop of the diagram 
is 70, and of the lower loop 5 lbs., and the engine fires 163 times per minute, 
what is the horse-power lost to mechanical friction? To fluid friction? 

Ans.y .000571, 1 H p.. .077 H.p. 

Problem 593. Compare by actual test the speed regulation of an engine 
working on the hit-and-miss principle with a throttling engine. Determine 
coefficient of regulation at full and half loads. 



290 * GAS ENGINE TESTING 60 

60. Economy Test of a Gas Engine 

Principles. A complete economy test of a gas engine should 
include, besides the fuel consumption, the determination of 
the various losses so that their distribution may be studied. 
All of the heat energy of the fuel supplied must be accounted 
for in the form of useful work and losses. The equation between 
these quantities is called the heat balance. 

The losses involved in the operation of a gas engine are as 
follows. Mechanical friction, heat carried away by jacket 
water, by the dry exhaust gases, by steam in the exhaust, by 
unburned fuel gas, and stray losses as radiation, etc. It is con- 
venient and logical to base the calculation of these losses upon 
1 cu. ft. of fuel gas under standard conditions of temperature 
and pressure. The heat balance may then be written, *^ heat 
supplied by 1 cu. ft. of gas equals the heat from 1 cu. ft. turned 
into useful work plus heat from 1 cu. ft. lost to friction 
plus, etc." 

To measure the useful work and friction and jacket losses 
on this basis it is necessary to meter the fuel supplied in a given 
time. The other quantities of the heat balance require the 
analyses of both the fuel and exhaust gases. Generally, for the 
fuel gas analysis, a chemist's services are needed. Strictly 
speaking, a fair sample of the gas used during the test should be 
analyzed, but when the fuel is such as cit}' illuminating gas 
which does not vary much from day to day, an average analysis 
is fairly representative and may be used without considerable 
error. 

The table, page 165, gives the average composition of the 
principal gas engine fuels. 

The exhaust gas analysis may be made with the Orsat appa- 
ratus. The chief constituents are CO2, O2, and N2, but an 
analysis for CO should not be omitted. A determination of 
H2 is desirable, but not necessary if the CO is less than 1 per 



60 GAS ENGINE TESTING 291 

cent, as it is in proper operation. Since the CO is the least 
readily burned of the fuel gas constituents, it is a fair assump- 
tion that the hydrogen and hydrocarbons are completely burned 
if the CO is nearly all burned, and experiment bears out this 
assumption. 

Knowing the fuel and exhaust gas analyses, the weights 
of gases in the exhaust pipe per cubic foot of fuel supphed may be 
calculated from the formulas deduced under Test 40 (6). This 
division should be re-read and thoroughly understood. 

Sampling. For a chemist's analysis of the fuel gas, it is 
best to take a continuous sample covering the whole time of the 
test. This can be done by connecting a 5-gal. flask with rubber 
tubing to the gas main and syphoning water from the flask at a 
slow and uniform rate thus drawing in the sample. Sampling 
for heat value determination may be made as described on 
page 178, Test 39. 

For throttling engines, the exhaust gas may be sampled as 
explained on page 193, Test 40. Hit-and-miss engines, it should 
be remembered, occasionally discharge air into the exhaust pipe 
which has not mixed wdth fuel. This air carries a certain amount 
of heat, though less than that carried by burned gases, and for 
this reason should be counted separately. It is possible to 
make an arrangement in the exhaust pipe by which the discharge 
from a missing stroke is by-passed and its temperature and quan- 
tity measured separately from the main exhaust. As this is a 
difficult matter, results may be obtained by averaging in the air 
from a missing stroke with the working exhaust, the sample 
then being taken as for a throttling engine. A thermometer 
in the exhaust pipe will show a mechanical average of the variable 
temperature w^hich may be used for calculating the heat lost. 
When the exhaust from a hit-and-miss engine is sampled in this 
way, the excess coefficient cannot be figured from the anal^^sis 
without first applying a correction for the air taken in by the 
engine, but not used to mix with the fuel. 



292 GAS ENGINE TESTING 60 

Since both the fuel and exhaust gases are generally under 
pressure, it is easier and more accurate to obtain samples than 
in boiler work. 

Duration of Test. This should be several hours, preferably, 
but, if on a small engine, a test of only one hom* long will give valid 
results if the engine is prcviousl^^run for fifteen or twenty minutes 
under the conditions to be maintained during the test. The 
readings to be mentioned later should be taken sufficiently 
often to obtain a fair average. The useful horse-power should 
be maintained at a constant value and all other conditions kept 
as uniform as possible. The test results are not valid unless 
the gas consumption is uniform as shoTMi b}' meter readings 
taken at equal time intervals. 

To make the methods clear, the measurements from a gas 
engine test will be worked through for the various results. Table 
No. 1 gives these measurements, and also the notation used in 
the formulas. The fuel used was illiuninating gas manufactured 
in S\Tacuse, an average anah'sis of which is given in columns 
(1) and (2) of Table No. 2. page 294. 

(a) Fuel Consumption, Cubic Feet of Gas per Brake horse- 
power-hour. Since the weight of fuel in a cubic foot varies 
with the pressure and temperature, the gas meter readings should 
be referred to standard conditions, namely, a pressure of 29.92 
ins. of mercury and a temperature of 32° F. The following 
formula may be used. (See Table No. 1 for notation.) 

B 



P and Tf necessitate the use of a water manometer and a ther- 
mometer at the point in the gas main where the gas meter is placed. 
For small size engines, the meter may be the usual gas meter, 
or a gasometer, but for large sizes, meters of the pitot, venturi, 
or orifice type may be used. When the engine is so large as to 



60 GAS ENGINE TESTING 293 

TABLE 1 

GIVING DATA FROM A GAS ENGINE TEST AND NOTATION 

USED IN FORMULAS 
B.h.p.= brake horse-power =25 , 

I.h.p. =net indicated horse-power =30. 1 

F.h.p. = friction horse-power 

F = number of cubic feet of fuel gas per hour, by meter =414 

y = ditto, corrected to absolute pressure of 29.92 ins. of mercury 

and 32° F. 
5 = Barometer reading, inches of mercury 29.5 

P = pressure of fuel gas above atmosphere, at meter, inches of 

water 4 

F = fuel consumption, standard cubic feet of gas per brake 

horse-power-hour 
TV = temperature of fuel gas at meter, degrees F. =68 

^y = temperature of ingoing jacket water, degrees F. =61 

TV = temperature of outgoing jacket water, degrees F. =133 

Te = temperature of exhaust gases, degrees F. =750 

t = temperature of air near engine, degrees F. = 70 

TF^ = weight of jacket water, pounds per hour =1210 

Vd = volume of dry exhaust gas from the combustion of 1 cu. ft. 

of fuel, cubic feet per cubic foot 
Wd= weight of dry exhaust gas from the combustion of 1 cu. ft. of 

fuel, pounds per standard cubic foot 
Wv = weight of water vapor, ditto 
i^= ratio by volume of air consumed to fuel gas 
X = excess coefficient 
Cj hf g = irom. sums of columns (3), (4), (5), Table 3, respectively. 

Volume Analysis of Exhaust Gas, Per Cents 

D = carbon dioxide, CO2 =9.0 

= oxygen, O2 =8.8 

M = carbon monoxide, CO =0.5 

F = hydrogen, H2 Not analyzed. 

A^ = nitrogen, N2 =81.7 

be inconvenient to brake, the useful horse-power may be approx- 
imated by subtracting from the indicated horse-power at the 
running load its value when the engine is running entirely free. 
Applying the data of Table No. 1, we have, 

y^ = 16.4X ^e . .in X414 = 385 cu. ft. per hour. 
68+460 



294 



GAS ENGINE TESTING 



60 



TABLE 2 

ANALYSIS OF FUEL GAS USED DURING TEST, AND COMPU- 
TATION OF QUANTITIES USED IN FIGURING RESULTS 



(1) 



(2) 



Constituents | Per Cent 
of Fuel. !by ^'olume. 



CO 

H2 

CH4 
C2H4 

CeHe 

O2 

CO2 

N2 



Sum 



23.5 
36.4 
15.3 

6.9 

3 

1 

4 

8 



(3) 



(4) 



Subscript of Ditto of H. 

CX(2). 



(5) 
Ditto of O. 



23.5 


72.8 


23.5 


15.3 


61.2 




13.8 


27.6 




23.4 


23.4 


'2.^'" 


4.2 





8.4 



80.2=c 



185.0=2/1 
/?-92.5 



34.7=2^ 
^ = 17.35 



(6) 

Higher 

Heat 

Value of (1) 



342 

348 

1065 

1680 

4000 



(7) 

(6) X(2) 
100 



80.5 
127 
163 
116 
156 



643 = 
higher heat value of 
fuel 



From which the fuel consumption is 
, 385 



25 



15.4 standard cubic feet per brake horse-power-hour. 



(b) Heat Supplied. Since the heat balance is based upon 
one cubic foot of the fuel gas, the heat supplied is its heating 
value. It is preferable to use a calorimeter for this determina- 
tion, such as the Junker, but if one is not available a working 
value may be obtained by calculation from the fuel gas analysis, 
Test 39 (c). The calculation is made in column 7 of Table 2. 

The gas engine code of the A.S.M.E. specifies that the 
'^ higher '' heat value be used, that is, the heat obtainable 
from the fuel including the latent heat of vaporization of the 
water formed by combustion of the hydrogen. Some authorities 
contend that the lower heat value is more logical to use in 
this connection since the gas engine cannot avail itself of this 



60 GAS ENGINE TESTING 295 

latent heat, but for the sake of uniformity the recommendations 
of the code will be followed. 

(c) Heat Converted into Useful Work. The heat equivalent 
of one brake horse-power-hour is 2545 B.t.u. Since the fuel 
consumed to produce this power is F cu. ft., the heat equivalent 
of the useful power per cubic foot of fuel is 

2545 

Applying the data of the example this is, 

2545 



15.4 



= 165 B.t.u. 



Dividing this by the heat value gives 25.6 per cent. This is 
the thermal efficiency. 

(d) Heat Lost to Mechanical Friction. In power units, 

F.h.p. = I.h.p.-B.h.p. 

To base this upon the heat of one cubic foot of fuel, a formula 
derived the same as the one last given is used, namely 

T. . ,. 1 T, ^ 2545 F.h.p. 
liriction loss, B.t.u. = - 



V 
Applying the data of the example, this is 

?M5|^).33.7B.t.„. 
or 33.7-^643 = 5.2 per cent. 

(e) Heat Lost to Jacket Water. This is the heat absorbed 
in a given time divided by the fuel used in the same time. Con- 
sidering hourly quantities. 

Jacket loss=' — ^-^, — —. 



296 GAS ENGINE TESTING 60 

The weight Wj may be measured by a barrel or tank on a plat- 
form scales. The temperatures should be read with two ther- 
mometers; one in the discharge tank (provided the piping is 
arranged to discharge without material radiation loss), the other 
in a thermometer well in the inlet pipe or in a receptacle drawing 
water from a tap in the main situated similarly to the jacket 
as to temperature. 

Applying the data of the example, 

, , ., 1210(133-61) ^o^-p. 
Jacket loss = -^r^ ^^^ =226 B.t.u. 

ooO 

or 226 -^ 643 = 35.2 per cent. 

(f) Volume of Dry Exhaust Gas per Cubic Foot of Fuel Gas. 
This quantity is to be used in the various calculations from the 
exhaust gas analysis. Under Test 40 (b) there is deduced the 
formula, 

' D+M' 

c is found as in column 3 of Table 2. The subscript of the C 
in each fuel gas constituent shown in column 1 is multipHed 
by the volume percentage of that constituent as shown by column 
2. Column 3 gives these products, the sum of which is the 
value of c. 

For the data of the example 

(g) Loss of Heat to Dry Exhaust Gases. This determina- 
tion involves the measurement of the temperature rise of the 
fuel and air mixing with it, and of the weight of the dry exhaust 
gases. For the specific heat, an average value, 0.245, may be 
used w^ith sufficient accuracy. Then 

Loss to dry exhaust gases = 0.245 Wd(Te — t). 



60 GAS ENGINE TESTING 297 

Under Test 40 (6) there is deduced the formula, 

TF<, = g^ I nD+80+7{M+N) I , 

by which the weight of the dry exhaust gas may be found from 
its analysis. 

The temperature in the exhaust pipe should be taken by a 
high reading thermometer (1000° F.) inserted in a well filled 
with fine, dry sand, located as near the engine as possible. 

Applying the data of the example, 

^y ^ 8.44{ 11 X9+8X8.8+7X (0.5+81.7)} 
^ 9000 ' 

= 0.703 lbs. per cu. ft. of fuel, 
and loss to dry exhaust gas = 0.245 X 0.703 X (750 -70) 

= 118B.t.u. 
or 118-4-643 = 18.3 percent. 

(h) Loss of Heat to Water Vapor in the Exhaust. Since the 
higher heat value of the fuel is used, the latent heat of the 
water vapor is to be included. The small amount of water 
vapor brought in as humidity of the air and fuel may be ignored, 
particularly as its latent heat is not added by the fuel. This 
leaves only the water from the combustion of hydrogen. A 
formula for the weight of vapor so formed from one cubic foot 
of fuel gas is deduced under Test 40 (6). Combining this with 
the expression for total heat of steam under the given condi- 
tions (see page 143), we have. 

Loss of heat to water vapor = TFoX (total heat of the vapor 
above room temperature) 

= 0.0005/1 (1090+0.46^6-0- 



298 GAS ENGINE TESTING 60 

The value of h is found similarly to c, as shown by column 4, 
Table 2. 

Applying the data of the example. 

Loss to water vapor = 0.0005X92.5X(1090+0.46X750-70) 

= 64.3 B.t.u. 
or 64.3 -^ 643 - 10 per cent. 

(i) Heat Lost by Unbumed Fuel Gas. The volume of 
unburned CO per cubic foot of fuel gas, according to Test 40 (6), 
is Vi = VdM -^100, As the heat value of CO is 342 B.t.u. per 
cubic foot, the 

Loss to unburned CO = 3.42 VaM. 

Similarly, if H per cent of hydrogen is found in the exhaust, 

Loss to unburned H2 = 3.46 VaHj 

the higher heat value of hydrogen being 346 B.t.u. 

These two expressions may be combined by assuming an 
average heat value, 344, to apply to both CO and H2. Then 

Loss to unburned CO and H2 = 3.44 Vd{M+H). 

If hydrogen has not been analyzed for, H may be omitted. 
Applying the data of the example, 

Loss to unburned fuel = 3.44X8.44X0.5 = 14.6 B.t.u. 

or 14.6 -^ 643 = 2.3 per cent. 

(j) Heat Lost to Radiation, etc., is found by subtracting from 
the heat value of the fuel the other quantities of the heat balance 
(c) to (j), or by subtracting from 100 per cent these quantities 
expressed in per cents. The unaccounted for heat includes that 
used for pumping the fuel mixture into the cylinder if the area 
of the lower loop has been subtracted from the upper of the 
indicator diagrams. This quantity could be separately measured, 



60 GAS ENGINE TESTING 299 

but it is generally sufficient to include it in the friction loss as 
is done when the lower loop is altogether ignored, or to list it 
under radiation. 

Applying the data of the example, 

Loss to radiation, etc. = 643-165-33.7-226-118-64.3-14.6 

= 21.4B.t.u., 
or 21.4-^643 = 3.4 per cent. 

(k) Cubic Feet of Air per Cubic Foot of Fuel Gas. This 
may be figured from the formula deduced under Test 40 (6), 

R={Vd{D+O+0,5M)+0.5h-g}-^21 

in which g is found under column 5, Table 2. 
Applying the data of the example, 

i2 = {8.44X(9.0+8.8+0.5X0.5)+0.5X92.5- 17.35} -=-21 
= 8.63 cu. ft. 

(1) The Excess Coefficient. The following formula may be 
used. 

__21^_ 

c+0.5h-g' 

Applying the data of the example, 

21X8.63 ^ 

80.2+0.5X92.5-17.35 

Problem 60i. The heat balance is found for a number of runs at differ- 
ent loads, and the items plotted thus: Eff. vs. B.h.p., Eff.+Friction vs. 
B.h.p., Eff. + Friction + Jacket loss vs. B.h.p., etc. Sketch the resulting 
curves in what you would expect to bo their form and give reasoning. 

Problem 6O2. If the air used in the test example given above w^as satu- 
rated with humidity, what would be the per cent loss to the heat carried 
away by this vapor? Ans.j 0.5%. 



300 GAS ENGINE TESTING 61 

61. Economy Test of an Automobile Engine 

Principles. Engines of this tj^po are variable speed. A 
complete test will therefore consist of enough runs at different 
speeds to cover the working range. As the rotative speeds are 
high, these engines cannot be indicated except with the optical 
indicator. The exhaust gas anal3'sis cannot always be relied 
upon for the determination of the losses, because irregular firing, 
incomplete combustion, or lubricating oil in the exhaust will 
make erroneous the percentages as usually found. If condi- 
tions are such that the exhaust gas analysis is valid, the methods 
of the preceding test and the formulas for coal combustion, 
Test 40 (6), are applicable. In these formulas, C^/ = Cz = weight, 
in pounds, of the carbon in the fuel per pound of fuel; since all 
the carbon is gasified. In the formula for the weight of water 
vapor in the exhaust, the value of m, moisture in the fuel, drops 
out. The results from the formulas wdll be based on 1 lb. of 
fuel. 

American gasoline, specific gravity about 0.7, contains roughly 
83 per cent of carbon, 15 per cent of hydrogen, and less than 
1 per cent of oxygen, by weight. Kerosene is a little higher in 
carbon and lower in hydrogen. The higher heat value of gaso- 
line is about 20,000 B.t.u.; the lower, about 19,000 B.t.u. per 
pound. The heat values of kerosene per pound are practically 
the same, but based on the gallon they are higher, the specific 
gravity of kerosene being 0.8 or more. 

(a) Determination of Torque and Brake Horse-power at 
Various Speeds. The ordinary Prony brake is difficult to use 
when it is sought to maintain a uniform load long enough for 
a fuel consumption test, because of the lack of uniformity of the 
frictional resistance. Fan brakes have been much used for 
the purpose, but they are not strictly reliable. Probably the 
best results ensue from the use of a well designed water brake. 
The writer has used a rope brake with considerable success. 



61 GAS ENGINE TESTING 301 

At each speed the carburetor and spark should be adjusted 
as under regular operation of the engine, so as to get the maxi- 
mum brake thrust without using an excess of fuel. If the fuel , 
consumption is not measured, each run should be at least fifteen 
minutes in duration after uniform conditions have been estab- 
lished. 

It is useful to plot both torque and brake horse-power against 
speed in revolutions per minute. 

The brake horse-power of automobile engines is often esti- 
mated by empirical formulas, especially for the purpose of rating. 
The Association of Licensed Automobile Manufacturers uses 
the formula 

B.h.p.=i)2X number of cylinders -^ 2.5, 

D being the bore in inches. This is referred to as the A.L.A.M. 
rating and applies to four-cycle engines at an assumed piston 
speed of 1000 feet per minute. It generally gives too high 
results. 

Under favorable conditions the mean effective pressure from 
the combustion of gasoline in the modern four-cycle engine is 
about 80 lbs. per square inch. Using this value and assuming 
a mechanical efficiency, a value for the brake horse-power may 
be calculated with which to compare test results. The mechan- 
ical efficiency may be estimated as follows. Compression is 
relieved from the cylinders by removing spark plugs, and the 
engine then caused to revolve as rapidly as convenient by pulling 
on a rope wrapped around the flywheel. The pull may be 
measured with a spring balance. From this measurement the 
torque necessary to overcome friction may be calculated. Assum- 
ing that the frictional torque remains constant, the mechanical 
efficiency equals 

Brake torque at given speed 
Brake torque at given speed -f- torque to friction* 



302 GAS PRODUCER TESTING 62 

(b) Fuel Consumption, Gallons or Pounds per Brake Horse- 
power-hour. The general principles of this determination are 
the same as for other fuel consumption tests except as regards 
the measurement of fuel. For this purpose a calibrated tank 
may be used, containing the oil with which to supply the engine. 
In some cases, it is desirable to keep the head of oil on the float 
valve of the carburetor practically constant. An arrangement 
may then be used similar, on a small scale, to that for measuring 
feed water to a boiler. Fig. 100. Another plan is to place the 
supply vessel on a scales and to syphon the fuel from it. 

Problem 61i. A 3-cylinder, 4-in.X4 in., 4-cycle engine develops 60 
Ib.-ft. torque at 800 R.p.m. The friction torque is 15 lb. -ft. What are the 
B.h.p., the probable mechanical efficiency and M.e.p.? Compare the B.h.p. 
Tith the A.L.A.M. rating, allowing for speed. Ans.j M.e.p. =75, 



62. Economy Test of a Gas Producer 

Principles. The distribution of the heat of the coal consumed 
by a producer is in four directions. First, the useful heat, 
appearing Us the calorific value of the dry, cool, gas; second, 
the heat carried by the gas as sensible heat and as latent heat 
of the excess steam; third, the heat lost to good fuel removed 
with ash; fourth, the heat lost through deposits of tar and soot, 
absorption and leakage of gases, and radiation from the producer. 

The selection of methods of measurement of these heat quan- 
tities is governed somewhat by the type of producer and fuel, 
whether pressure or suction, anthracite or bituminous. In any 
case, it is necessary to measure the coal and ash during a test of 
sufficient duration, and to provide a proximate analysis of the coal 
and a chemist's analysis of an average sample of the gas. The 
gas usually contains between 10 and 20 per cent of hydrogen, 
1 to 3 per cent of marsh gas, and a small amount of defiant 
gas, in addition to CO2, CO, and N2. These make it not easy 



62 GAS PRODUCER TESTING 303 

to analyze, although it may be done without much labor if the 
apparatus is available. 

The calorific values of both coal and gas may be calculated 
from their analyses. 

The volume of gas generated may be figured from the gas 
analysis with acceptable accuracy in most cases, thus dispensing 
with the bothersome meter question. This calculation depends 
upon the assumption that all the carbon gasified from the fuel 
appears in the gas analysis. It is therefore approximate since 
the condensible hydrocarbons distilled from the coal throw 
down some carbon in the form of tar, and some disappears as 
soot. In the case of anthracite gas, or well fixed bituminous, 
this is neghgibly small since, generally, it does not involve more 
error than is inherent to the coal measurement. 

The largest error likely to occur is in the measurement of 
the coal consumed, in that the producer may contain a very 
. different amount at the end of the test from its contents at the 
beginning. To avoid this, the conditions of the producer at 
starting and stopping should be noted and made in all respects 
as nearly the same as is possible. Starting and stopping should be 
be timed just after a regular cleaning. The duration of the test 
should be long enough to reduce the probable error caused by 
the variation in fuel content of the producer to a small percentage 
of the total coal fired, which, in general, will not be less than 
twelve hours. If the weight of each charge of coal is plotted 
as a total against the time at which it is consumed, the result- 
ing curve will show by its straightness the uniformity of coal 
consumption. For such uniformity all external conditions 
must be kept as constant as possible and the producer should 
be run for some hours under the required conditions before the 
main test is started. 

The ash and refuse should be collected at regular cleaning 
intervals and weighed after drying. It is best to secure a sample 
of the total refuse just before weighing and to determine its 



304 GAS PRODUCER TESTING 62 

moisture and carbon as in the proximate analysis of the coal. 
It is often awkward to drj^ all the refuse thoroughly, but, if the 
percentage of moisture is known, the weight of dry refuse may be 
readil}" figured. 

Sampling of the coal and ash should be done as for a boiler 
test. Sampling of the gas should be the same as for the fuel 
gas during a gas engine test (see page 178). The gas should be 
collected before entering the scrubber, and after leaving it if 
it is desired to find the effect of absorption or leakage. 

The weight of steam furnished to a suction producer exclu- 
sive of that due to vapor in the air and moisture in the coal maj^ 
be found by supplying the vaporizer with water from a calibrated 
vessel and collecting and weighing the overflow. For a pressure 
producer, an orifice or nozzle method may be used to meter the 
steam, or it may be measured by weighing the feed water evap- 
orated b}' the auxiliar>^ boiler. 

The calculations from the test of an anthracite suction pro- 
ducer plant will first be given and then the modifications neces- 
sary for other types. Tables 1 and 2, pages 305 and 306, give 
the required test data together with the notation used in the 
formulas. The data are part of the full observations of a test 
reported in the Journal of the A.S.M.E., December, 1909, for 
which the ultimate as well as the proximate coal analysis and 
calorimetric determinations of fuel and gas were made, and the 
gas metered. The reader may thus compare the results by the 
approximate methods to be presented with the more exact 
results of the report.* 

All the items of the heat balance will l)e figured on the basis 
of 1 lb. of drv coal. The calorific value of the drv coal will thus 



* Note that these results are given for the standard gas condition of 
62° F. and 30 ins. of mercury, whereas the standard here used is for 32° F. 
and 29.92 ins. The volume per pound of the latter is 0.943 times that of the 
former. Also the specific heats of the gases are different, the values here 
quoted being by later authorities. 



62 GAS PRODUCER TESTING 305 

Table 1 

GIVING DATA FROM A SUCTION GAS PRODUCER TEST AND 
NOTATION USED IN FORMULAS 

Total weight of coal charged, pounds = 798 
Total weight of ash and refuse, pounds = 85 
Total weight of water used in vaporizer =268 

Proximate Analysis of the Coal. Per Cents by Weight of the Coal 

AS Fired 

Moisture =2.75 

Volatile matter = 6 . 00 
Fixed carbon = 78 . 45 
Ash =12.8 

m, vm, /c = weights of moisture, volatile matter, and fixed carbon per pound 
of dry coal, respectively. 
Weight of carbon in 1 lb. of dry refuse, pounds= 0.388 
Tj; = temperature of gas leaving producer, degrees F. = 1108 
<= temperature of fire room, degrees F. =82 

Ci = total weight of carbon in 1 lb. of dry coal, pounds. 
Ca= weight of carbon wasted in ash, per pound dry coal, pounds. 
Cf^ = weight of carbon gasified per pound dry coal, pounds, 
c, p = sums of columns 3 and 5, Table 2, respectively. 
F = volume of dry gas generated per pound of dry coal, standard 
cubic feet. 
1^2?= weight of the producer gas per pound of dry coal, pounds. 
TTa = weight of the air furnished per pound of dry coal, pounds. 
1^5 = weight of steam furnished per pound of dry coal, from the 

vaporizer, pounds. 
!:;« = weight of steam not dissociated per pound of dry coal, pounds. 

be the heat supplied; the sensible heat carried in by air, water, 
etc., being neglected. 

The principles upon which most of the calculations depend 
are given under Test 40 (6), coal combustion, and should be 
thoroughly understood. 

(a) Quantities to be Found Prior to Calculation of the Results. 
The proximate analysis of the coal should be based upon its dry 
weight. This calculation is the same as for Test 54 (c), as is 
that for Ctj the total carbon per pound of dry coal; since the same 



306 



GAS PRODUCER TESTING 



62 



Table 2 

ANALYSIS OF GAS GENERATED DURING TEST, AND COMPUTA- 
TION OF QUANTITIES USED IN FIGURING RESULTS 



(1) 

Constit- 
uents of 
Gas. 



CO 

H2 
CH4 
C2H4 

O2 
CO2 

Na 



(2) 

Percentage 

by 

Volume. 



27.0 
10.4 
1.8 
0.0 
0.2 
4.2 
56.4 



(3) 

Subscrint 
of CX(2) 



c = 33.0 



(4) 

Molecular 
Wt. of (1). 



27.0 


28 





2 


1.8 


16 





28 




32 


4.2 


44 


.... 


28 



(5) 
(2)X(4) 



756 
20.8 
28.8 


6.4 

184.8 

1579.2 



p = 2576.0 



(0) 

Higher Hoat 
Value of (1). 



342 

348 

1065 

1680 



(7) 

(6)X(2) 
100 



92.4 
36.2 
19.2 




147.8 = 
higher heat value of 
gas 



fuel analysis has been assumed. The methods of finding Ca 
and Cg are also the same as given under Test 54 (c). For the 
data given by Table 1, 

Total weight of dry coal consumed = 798 -0.0275X798 

= 776 lbs. 



and 



^^^85X0^^Q^Q^2 lb. 



776 



The carbon gasified is 



Cg = Ct-Ca = 0.81G - 0.042 = 0.774 lb. per pound of dry coal. 



The volume of dry gas generated per pound of dry coal, 
under standard conditions of pressure and temperature, may 
be found from a formula derived similarly to that for Vdj page 
198. For producer work D+M becomes c since carbon may 



62 GAS PRODUCER TESTING .307 

exist in other gases than CO2 and CO. c is found as shown in 
column 3 of Table 2. Then 



For the given data, 



2980 C, 



^, 2980X0.774 .^ n f+ ^u a 1 

V= ^^ = 69.9 cu. ft. per lb. dry coal. 

The weight of dry gas per pound of dry coal may be obtained 
from its volum.e if the weight of a cubic foot of the gas is known. 
For the latter quantity, the method of finding the density of a gas 
described on page 197 may be used. The weight of a molecule- 
foot of the producer gas is p-^ 100, p being determined as in column 
5, Table 2. The weight of a molecule-foot of hydrogen is 2, 
and its density under standard conditions is approximately 0.0056. 
Consequently, 

Density of dry producer gas = 0.0056 X^^^^ = 0.000028p. 

For the given data, 

Density of producer gas - 0.000028 X 2576 

= 0.0721 lb. per cubic foot, 

from which the weight of the dry producer gas per pound of dry 
coal is 

TF^ = 0.0721X69.9 = 5.04 lbs. 

The volume of gas may also be obtained by metering it 
through the whole test, but the method outlined above will 
generally be found sufficiently accurate if reasonable care is taken 
in the sampling and analysis of the gas. 

The weight of air supplied to the producer per pound of dry 
coal may be found from an expression similar to that for Wa for 



308 GAS PRODUCER TESTING 62 

coal combustion, page 199; the quantitj^ D+M being replaced 
by c. The formula then is, 

3MxN2XCg 

vY a J 



N2 being the per cent by volume of nitrogen in the gas as given 
in column 2, Table 2. For the given data, 

^, 3.04X56.4X0.774 . ^. ., 
Wa = 23 "" ^-^^ ^^• 

The weight of steam supplied by the vaporizer per pound of 
dry coal is found by dividing the total weight of water to the 
vaporizer by total weight of dry coal. For the given data, 

TF. = ^ = 0.345 lb. 

Coming now to the heat balance, the first item is 
(b) Useful Heat in the Cool Gas. This is exclusive of sensible 
heat if the gas is to be used for power, and is due to its calorific 
value when completely burned. The higher heat value will 
be used. Since all items of the heat balance are based on 1 lb. 
of coal, the useful heat may be found by multiplj^ing the volume 
of gas per pound of coal, V, by the higher heat value in B.t.u. 
per standard cubic foot. The heat value may be figured as in 
column 7 of Table 2. This gives the heat values of the gas con- 
stituents, according to their amounts in one cubic foot, the sum 
of which is the required heat value. For the given data, 

Useful heat = 69.9X148 = 10,300 B.t.u. 

The heat value of the dry coal was found to be 13,040 B.t.u., 
so the useful heat is 10,300^13,040 = 79.0 per cent. This is 
the ^^ cold gas " efficiency of the producer. 



62 



GAS PRODUCER TESTING 



309 



uoo 


. 




r 




— 


r— 










" 




J 


T 


























I 


/ 








«5 






















/ 










X 




















/ 












o0,30 
















/^ 


























^^ 


^ 




























^ 


r^ 




















ci 






^ 


y 


























^ 


^ 




























n?c; 








_^ 

























30 



(c) Sensible Heat in the Dry Gas Leaving the Producer 

is equal to 

TTpX specific heatX(T2,-0. 

The weight of the dry gas, Wv, has been previously figured. 

The specific heat of producer gas, varies greatly with the 
hydrogen content. Except for hydrogen the average specific 
heat of all the gases, exclusive of steam, may be taken as 0.26 
for a temperature of 1100'' or 
1200° F. The specific heat of 
hydrogen for these temperatures 
is about 3.72, so that even though 
its per cent by weight is always 
small the effect of hydrogen upon 
the average specific heat of pro- 
ducer gas is very marked and varies 
with the amount of hydrogen 
present. The curve, Fig. 104, gives 

the average specific heat of normal producer gas with various 
percentages of hydrogen. For the given data (^2 = 10.4 per 
cent) it is seen to be 0.288. 

The temperature of the gas should be taken near the outlet 
at the producer with a suitable pyrometer. 

For the given data. 

Sensible heat = 5.04 X 0.288 X (1108 -82) = 1490 B.t.u. 
or 1490^13,040 = 11.4 per cent. 

(d) Heat Lost by Excess of Steam to the Producer. This 
is estimated from the weight of steam found in the gas per pound 
of dry coal, and equals 



ID 20 

Per Cent Hg 

Fig. 104.— Specific Heat of 
Producer Gas. 



u'sX total heat per pound of the steam above feed temperature. 



310 GAS PRODUCER TESTING 62 

The total heat of the steam may be taken with sufficient accuracy 
for this calculation as 

1000+0.5 XTp. 

For a more exact value, the expression quoted on page 143 
may be used. 

To find Ws several methods may be used. It may be meas- 
ured directly by drawing a sample of the producer gas through a 
tube of calcium chloride, the increase of weight of w^hich gives 
the moisture absorbed. The gas is syphoned into a container of 
known size so that its volume, and hence its weight, may be 
obtained. iCs may also be figured from the hydrogen content 
of the coal and the gas. An easier method is based upon the 
fact that the sum of the weights of the gasified carbon, air, and 
water vapor fed into the producer must equal the weight of the 
producer gas including moisture. Hence, 

Co+Wa+Ws+m+YSipor brought in with tiir — Wp = Ws* 

The air vapor may be neglected here, although it may be a large 
percentage of the total steam, since its latent heat is not added 
by the coal. Then, for the given data, 

^., = 0.774+4.02+0.345+0.0283-5.04 = 0.137 lb., 

from which the heat lost to steam is 

0.137X(1000+0.5Xll08)=213B.t.u. 

or 21 3 -^ 13,040 = 1.6 per cent. 

(e) Heat Transferred to Scrubber Water. Items (c) and 
(d) together equal the heat given to the scrubber plus the heat 
radiated between the scrubber and producer outlets. For 
purposes of comparison, or to get an estimate of the amount of 



^55^^ 



62 GAS PRODUCER TESTING 311 

sensible and latent heat in the gas without measuring it as just 
described, the heat added to the scrubber water may be deter- 
mined. The water may be measured by a meter, and its tem- 
perature as for the jacket water of a gas engine. In the test 
quoted the total weight of scrubber water was 22,200 lbs. and 
its temperature rise was 45.8° F. Hence, the heat given to the 
scnibb9r per pound of dry coal is, 

^-^^X45.8 = 1310B.tu. 

(f) The Heat Lost to Carbon in the Ash. Taking the heat 
value of carbon as 14^600 B.t.u., this loss, per pound of dry coal 
is 

14,600 XCa. 
For the given data, 

14,600X0.042 = 613 B.t.u. 
or 613 -T- 13,040 = 4.7 per cent. 

(g) Radiation from the Producer and other Losses. These 
may be grouped in one item by subtracting the previously 
calculated heat balance quantities from the heat supplied, or 
some of them may be separately determined. The loss by leakage 
of air in the case of a suction producer plant may be found by 
comparing the useful heat, as herein calculated, before and 
after the dilution. In a pressure producer plant, any leakage 
is apt to be detected; the only way to measure it is by metering 
the gas since leakage does not alter its composition. The loss 
due to tar and soot may be found by a special analysis of the gas 
as it leaves the producer. 

Grouping these losses for the given data, we have 

Radiation, etc. = 100- (79.0+11.4+1.6+4.7) =3.3 per cent. 



312 GAS PRODUCER TESTING 62 

(h) Other Efficiencies and Results. The "hot gas" efficiency 
is often expressed when the gas is used for heating. In this 
case the sensible heat is also '^ useful.'' If, then, the first three 
items of the heat balance in per cent are added, the result will 
be the hot gas efficiency. For the given data, this is 

79.0+11.4+1.6 = 92.0 per cent. 

The " efficiency based on combustible," corresponding to 
the boiler efficiency so known, is the efficiency that would be 
obtained if there were no loss of fuel in the ash, and equals 

Eff . based on coal ^ ( 1 yt ) > 

\ vm+jcj 

the quantity in the parenthesis being the efficiency of the grate, 
or cleaning. For the given data, this efficiency equals 

for the cold gas. 

For purposes of comparison of tests with different kinds of 
fuel, it is useful to obtain the volume of gas per pound of com- 
bustible. This equals V -r- {vm +/c) . 

In capacity tests, the output may be measured in cubic feet 
per hour by multiplying F, as herein calculated, by the weight 
of dry coal used per hour. 

For pressure producers it is necessary to account for the 
coal used in the auxiliary boiler to make steam. This may be 
included in the total coal charged against the producer, and 
another item added to the heat balance to account for the heat 
lost in the steam making process. Or we may subtract from the 
volume of gas generated an amount equivalent to the steam 
supplied, which does not seem to be so logical a process. 



63 TESTING REFRIGERATION MACHINERY 313 

For bituminous producers, if much carbon disappears as tar, 
it is necessary either to meter the gas to get F, or to determine 
the amount of carbon going to tar from 1 lb. of dry coal, by 
analysis of a sample extracted from a measured volume of gas. 
From this result a more correct value of the carbon gasified is 
obtainable. 

The heat balance may be extended to cover the distribu- 
tion of heat in a gas engine supplied by the producer, by the 
methods indicated under Test 57 covering this subject. In 
this case the gas need not be metered, since the fuel quantities 
are measured as coal, and the heat quantities should be based 
upon 1 lb. of dry coal instead of 1 cu. ft. of gas. The exhaust 
losses as calculated under Test 57 may be readily changed to the 
coal basis by multiplying them by V as herein obtained. 

Problem 62i. Using the data of the test example, what is the percentage 
of heat radiated from the scrubber and immediate piping? 

Problem 62.2. Assuming that the engine of the example under Test 60 
was operated with gas from the producer of the example of Test 62 with the 
same engine heat balance items, calculate these items in per cents of the 
heat value of the dry coal. 

63. Test of a Refrigeration Plant * 
(Ammonia Compression System) 

Principles. The student, it is assumed, is informed upon the 
mechanical and thermal features of the ammonia refrigerating 
machine, descriptions of which are available in numerous treatises. 

Following are given definitions of the quantities usually sought 
in tests of refrigerating machinery. 

Refrigerating Effect is the amoimt of heat abstracted by the 
ammonia from the cooling medium, as brine, expressed in B.t.u. 
per unit of time (minute, hour or twenty-four-hour day). This 
includes the waste cooling effect due to heat transferred from 

* This and the two following tests are enlarged from a series by the author, 
in Powevy Sept. 19, Oct. 10, 1916, and April 10, 1917. 



314 TESTINXt refrigeration machinery 63 

bodies it is not desired to cool — a waste necessarily ensuing from 
imperfect insulation, manipulation, etc. 

The Unit of Refrigeration is a refrigerating efifect of 288,000 
B.t.u. per twenty-four hours, or 200 B.t.u. per minute. To 
obtain this effect by ice at 32° F., it would be necessarj^ to melt 
1 ton (2000 lbs.) of it in twenty-four hours, the latent heat of ice 
being 144 B.t.u. Units of refrigeration are therefore spoken of 
as tons more conmionly than as B.t.u. 

The Capacity of a plant equals the number of units of refriger- 
ation it delivers: That is, the number of tons of 32° ice it would be 
necessar}' to melt per twent3'-four-hour day to produce a refriger- 
ating effect equivalent to that of the ammonia. Hence, this 
quantity is often referred to as '* ice-melting capacity.'' 

Ice-making Capacity is sometimes considered in the case of 
plants devoted exclusively to the manufacture of ice. Expressed 
in tons per twenty-four hom's, this is equal to between one-half 
and eight-tenths of the ice-melting capacity" pre\'iously defined, 
the diminution l^eing due to the losses in the process of heat 
abstraction b\^ the brine, manipulations of cans, and to the fact 
that the water must first be cooled to 32° and after freezing, be 
chilled below that point. Rating m terms of ice-making capacity 
is therefore onl}' definite when the temperatures of water and 
finished ice are stated. 

The Coefficient of Performance is a more correct term for what 
is sometimes miscalled the efficiency of a refrigerating sj'stem. 
This quantity is the ratio of the refrigerating effect in B.t.u. per 
unit of time to the heat equivalent to the indicated work done 
by the compressor in the same time; that is, it is the useful effect 
divided by the power put in, and in this respect is superficiall}- 
an efficiency. The term efficienc}' generally has reference to the 
relation of an energ}', after passing through a conversion, to its 
value at the source. In the case of refrigerating machiner>^ 
the compressor energ}' is not the source of the useful effect. In 
reality, it is the condensing water that does the coohng, the com- 



63 TESTING REFRIGERATION MACHINERY 315 

pressor being merely an auxiliary in the process. As the work 
done upon the ammonia is the paid-for item and as the re- 
frigerating effect is the thing desired, it is useful to know the 
ratio of the two. 

The Ideal Coefficient of Performance is the maximum that could 
be obtained under a given set of operating conditions if there were 
no losses. It is fixed by the operating temperatures of condenser 
and refrigerator and is equal to 

460+ Tr 
' Tc-Tr' 

in which the numerator is the absolute temperature of the refrig- 
erator, Tt is its temperature in degrees Fahrenheit, and Tc is 
the temperature of the condenser in the same units. It should 
be noticed that neither refrigerator nor condenser is ever at one 
uniform temperature in operation. To maintain the heat flow, 
the brine must always be a little warmer than the ammonia it 
boils, and the circulating water always a little cooler than the 
vapor it condenses. But, assuming ideal apparatus, the ammonia 
vapor could be worked in the refrigerator up to the temperature 
of the outgoing brine (just as in a perfect steam boiler the steam 
might be worked up to the temperature of the outgoing flue gases), 
and in the condenser the vapor could be worked down to the tem- 
perature of the outgoing water. If these temperatures be used in 
the calculation, then, the resulting coefficient of performance 
represents ideal conditions of the whole system, including heat 
transmission of refrigerator and condenser. If, however, the 
temperatures corresponding to the vapor pressures of the am- 
monia are used, the resulting coefficient is that of the system, 
exclusive of losses in heat transmission in refrigerator and con- 
denser. Numerical examples of these two values of the ideal 
coefficient of performance will be cited later. 

The Efficiency of the plant may be expressed as the ratio of 
the actual to the ideal coefficient of performance. 



316 TESTING REFRIGERATIOX AIACHIXERY 63 

The Economy of compression plants is often stated in pounds 
of refrigerating effect (ice-melting) per pound of coal, on the 
assumption that a certain number of pounds of coal are con- 
sumed to make one indicated horse-power at the compressor. 

Other Results should include the expense of condensing water 
(under certain conditions this may be as large as the cost of the 
fuel) and the cost of auxiliary powder. 

For complete tests, enabhng a stud}^ of all the heat transfers, 
temperature and time-quantity determination should be made of 
both ammonia and cooling water. 

The Duration of the trial should be at least twelve hours, and 
preferably twenty-four, to allow for the possible error at the 
finish of the test due to a different amount of heat being stored 
in the refrigerator, condenser, etc., from that contained at the 
beginning. 

(a) Refrigerating Effect by Measurement of the Brine. Re- 
frigerating effect in B.t.u. per minute, equals 

R = W{T-t)C 
in which 

Tr = weight of brine in pounds per minute; 
r = temperature of brine at inlet in degrees Fahrenheit; 
^ = temperature of brine at outlet in degrees Fahrenheit; 
C = specific heat of brine. 

For the determination of W the various methods of water 
measurement have been applied. Owing to the large quantit}' 
of brine circulated even in small plants, the method of direct 
weighing Ij}^ tanks and scales is inconvenient. A modification 
of this consists in running the brine through two tanks, one above 
the other, the upper one having in its bottom a number of orifices 
through which the brine flows. The rate of flow varies with the 
lieight of the brine level in the upper tank. One of the orifices 
may be i-eadily calibrated during the trial b}^ collecting, weighing 



63 TESTING REFRIGERATION MACHINERY 317 

and timing its discharge at various heads. The total brine flowing 
through all the orifices may then be found by multiplication. 

When meters calibrated in gallons or cubic feet are used, a 
separate determination of the weight of the brine per gallon or 
cubic foot is necessary. This may be made with a hydrometer, 
care being taken to test a sample withdrawn near the meter 
and at approximately the same temperature as it has in the 
pipe. 

Concerning temperatures T and t, as the range is only between 
5 and 10°, finely graduated thermometers must be used. For 
not more than 2 per cent of error the graduations must be about 
2 per cent of the temperature range — that is, between one-fifth 
and one-tenth degree. The thermometers should be inserted in 
wells filled with mercury or oil and should be located in the inlet 
and outlet pipes as near as possible to the cooler. The protruding 
portions of the wells should be well insulated. During the trial 
it is well to interchange the thermometers as a check on their 
accuracy. 

The Specific Heat of Brine varies with its concentration, con- 
stituents and temperature. The last-named variation is com- 
paratively small — about 0.05 per cent decrease of the specific heat~ 
for each degree decrease in temperature. As to the effect of the 
constituents, the presence in calcium chloride brine of manganese 
and sodium chloride in moderate quantities (say up to 20 per cent) 
does not affect the specific heat of the mixture materially. The 
effect of the concentration, however, is to lower the specific heat 
from unity (that of water) down to about 0.65 at a concentration 
corresponding to a specific gravity of 1.26. 

The following formula for pure calcium chloride brine will give 
results for the specific heat of commercial calcium chloride brine 
to within 1 or 2 per cent of error, between the limits of —4 and 
40° F., and specific gravities between 1.10 and 1.26: 

C=1.833~0.93(?-0.0005(32-ra). 



318 TESTING REFRIGERATION :\IACHINERY 63 

In this formula* G is the specific gravit}', and Ta is the average 
temperature of the brine in degrees Fahrenheit at inlet and outlet. 

(b) Refrigerating Effect by Ammonia Measurements. The 
heat added to the ammonia in the brine cooler equals the heat 
lost by the brine. If the former quantity be found it is therefore 
a measure of the refrigerating effect, and we can put 

in which R is as before, A is the number of pounds of anhj^drous 
ammonia circulated per minute, and 

H = the total heat of the ammonia per pound leaving the cooler, 
h' = the heat of the liquid at the expansion valve. 

To find A, see Test 64 (h). 

H and h^ are to be found from tables of the properties of 
ammonia, t or from the ]\Iollier diagram for ammonia. To use 
these tables, the same data as for steam are necessary. For H 
the suction pressure must be read, together with the temperature, 
so that the heat of superheat may be calculated. The specific 
heat of superheated ammonia at low pressures may be taken as 
0.51. For /i', the head pressure may be referred to. 

It is difficult to get the exact amount of superheat of the 
ammonia leaving the cooler, and also to maintain a uniform 
quantity of ammonia in the cooler to avoid the error of starting 
and stopping as in a boiler test. For these reasons the refrigerating 
effect as obtained by this method may be expected only roughly 
to check the result by the brine method which is therefore to be 
preferred. 

When the cooling is done by the direct expansion of ammonia, 
there is no choice between these methods, as brine measurements 
are eliminated under such conditions. An approximation of the 

* Deduced from the values given in Bureau of Standards Bulletin No. 135. 
t See Appendix for properties of saturated ammonia. 



63 TESTING REFRIGERATION MACHINERY 319 

refrigerating effect can be made by still another method which is 
also useful as a rough check of either (a) or (b) . 

(c) Approximate Calculation of Refrigerating Effect. Neglect- 
ing effects of radiation, etc., the heat added in the refrigerating 
plant equals the heat equivalent to the compressor work, plus 
the heat added to the ammonia, R. This sum equals the heat 
taken awa}^, or the heat imparted to circulating water. By finding 
the heat taken up by the condenser water and jackets and sub- 
tracting from this the heat equivalent to the compressor work, we 
thus have a rough measure of the refrigerating effect. 

The condenser * water may be measured as under (g). Its 
temperature rise should be obtained by thermometers at inlet 
and outlet, from which data the heat removed may be calculated. 

(d) Ice-melting Capacity is readily calculated from the value 
of the refrigerating effect R in B.t.u. per minute, by dividing by 
200, the result being in tons per twenty-four hours. 

(e) To obtain the actual coefficient of performance, it is neces- 
sary to indicate the comipressor. The process here is similar to 
that ^or steam-engine trials and hardly needs comment other than 
that a special steel-lined indicator must be used with as short 
pipe connections as possible to avoid materially increasing the 
clearance space. Having obtained the indicated horse-power of 
the compressor, the coefficient sought is 



42.4Xl.h.p.' 



(f) The Ideal Coffiecient of Performance may be found from 
the average thermometer readings at the brine and condenser 
water outlets, as previously defined. Or, if vapor pressures are 
used, the corresponding temperatures may be found from the 
ammonia tables. When the plant is equipped with pressure 
gages bearing thermometric scales, the ammonia tables may be 
dispensed with. 



320 TESTING REFRIGERATION :MACHINERY 63 

As an illustration of the difference that may exist between the 
values of the ideal coefficient as obtained by the two methods 
previously discussed, consider the following data: 

Suction pressure, 28-lb. gage; from tables, temperature, 
15°; head pressure, 151-lb. gage; from tables, temperature, 
84.5°; outgoing brine temperature, 28.9°; outgoing condenser- 
water temperature, 83.5°. 

From these figures the ideal coefficient of the whole sj^stem is 

460+28.9 _ 
83.5-28.9 ^-^^ 

and for the system, exclusive of condenser and refrigerator trans- 
mission losses, is 

460+15 



84.5-15 



= 6.83. 



(g) Gallons of Cooling Water per Minute per Ton. The 
measurement of the condenser water is simpler than that of the 
brine, the quantity being much less. Direct weighing or the 
usual forms of water meter may be emploj-ed, care being taken to 
select one appropriate to the conditions of flow, whether pulsating 
or steady. The number of gallons of cooling water per minute 
per ton of ice-melting capacity should be figured for purposes of 
comparison and also in order to add the cost of this item to the 
other costs to obtain the total. This item should include all 
cooling water used, such as compressor jacket water and water 
to steam condenser if one is used. 

(h) Overall Economy. The performance of auxiliaries may 
be either estimated or measured. When the}^ and the com- 
pressor are steam driven, it is well to measure the total steam 
supplied to the plant b}' the boiler-feed method or b}^ a steam meter 
installed so as to avoid inaccuracies due to pulsating flow. The 
steam consumption of the compressor and of the whole plant may 
then be stated in pounds of steam per ton of ice-melting. 



''•^ 



63 TESTING REFRIGERATION MACHINERY 321 

Ratings are generally based on head and suction pressures of 
185 and 15.3 gage respectively, corresponding to temperatures 
of C6 and 0° F., respectively. Any departure from these con- 
ditions should be considered in making comparisons of test results'. 

Problem 63i. What is the tonnage (ice-melting capacity) of a plant that 
circulates 6000 lbs. of brine (specific heat = 0.80) per hour at an average tem- 
perature fall ofl5°F.? Ans. Q tons. 

Problem 682. What is the specific heat of a calcium chloride brine having 
a specific gravity of 1.2, if its temperature is 32° F.? If its temperature is 
0° F.? Ans., 0.717; 0.701. 

Problem 683. Supposing 600 lbs. of anhydrous ammonia are circulated 
per hour at a head pressure of 160 lbs. gage, and a suction pressure of 20 lbs. 
gage, the superheat being 25°; what should be the refrigerating effect? 

Ans., 29,600 B.t.u. per hr. 

Problem 684. A refrigerating plant uses 14,220 lbs. of water per hour in the 
ammonia condenser, with average incoming and outgoing temperatures of 
50° and 75°, respectively. The I.h.p. of the compressor is 20. Approxi- 
mately what is the tonnage (ice-melting capacity)? Ans. 25 A tons. 

Problem 685. What is the actual coefficient of performance for the data 
of Problem 684? Ans. 6. 



64. Test of a Refrigeration Plant. 

(Ammonia Absorption System) 

Principles. In some respects the results from and methods 
for the test of an absorption plant are identical to those applying 
to the compression system, for which, see Test 63. The capacity 
in terms of ice-melting effect may be found in the same way, and 
the investigation of the condenser operation is the same. The 
actual coefficient of performance may not readily be obtained, 
since the energy imparted to the ammonia (barring the work of 
the ammonia pump, which is comparatively small) is in the form 
of heat instead of compressor work. But the ideal coefficient of 
performance may be determined as for a compression plant and 
may be useful for purposes of comparison of the two systems. 

The principal economy result is the steam consumption 
expressed in pounds of steam per hour per ton of refrigerating 



322 TESTING REFRIGERATION MACHINERY 64 

effect. This may be determined in toto for the plant or itemized 
as live steam to the pump and steam to the generator, the latter 
being subdivided into live and exhaust steam according to whether 
the one or the other or a combination is used. Under favorable 
circumstances the generator will use 30 lbs. of steam per hour per 
ton. The steam consumption of ammonia pumps is subject to 
wide variations due to their construction. Although the energy 
delivered is small compared with the heat transferred in the 
generator, a test of this pump should be included in economy 
trials because of the bearing of its performance on the steam 
consumption of the plant; and the pump test should preferably 
include a determination of the horse-power delivered. 

In addition to these results it is desirable to ascertain the con- 
dition of the aqua ammonia and, if convenient, the amount of 
anhydrous circulated per unit of time. The former is expressed 
in terms of its concentration; that is, the part of a pound of 
ammonia in one pound of the aqua ammonia (more frequently 
expressed as a percentage). The concentration results show the 
working of the absorber and generator and enable calculations 
regarding the ammonia circulation. 

(a) Refrigerating Effect, 2 methods. See Test 63, (a) and (b). 

(b) Ice-melting Capacity. See Test 63, (d). 

(c) Ideal Coefficient of Performance. See Test 63 (/). 

(d) Gallons of Cooling Water per Minute per Ton. See Test 
63 {g) in so far as condenser water is concerned. All other cooling 
water supplied, if in separate amounts, should be included in this 
total, b}' similar methods of measurement. 

(e) The Steam Consumed by the Generator is readily ascer- 
tained by piping the generator-trap discharge into a weighing 
barrel. The barrel, to start with, should be about half full of 
cold water to prevent evaporation of the condensate from the 
trap. Quick emptying should be provided for. Weights should 
be recorded at uniform time intervals (to show uniformity of 
operation), from which data the rate in pounds per hour may be had. 



64 TESTING REFRIGERATION MACHINERY 323 

Quality determinations of the steam are important, unless an 
efficient separator is installed to remove the moisture from the 
incoming steam, to the consideration of the results, as also are 
pressure readings. 

If reduced hve steam is used in addition to exhaust and it is 
sought to measure them separately, a steam meter may be appHed 
to the live-steam line. The exhaust-steam quantity then equals 
the total trap condensate minus the meter reading. Measure- 
ment of the feed water, as for a boiler test, may also be resorted 
to, in cases where the plant may be isolated. 

^ATien the generator is supplied with exhaust steam from the 
pumps plus reduced live steam, the hve steam may be found by 
subtracting from the generator trap discharge the steam con- 
sumed by the pumps. This last may be measured as follows: 

(f) Steam Used by Ammonia and Brine pumps. A separate 
test should be made to determine this, but if conditions are not 
favorable, the steam required to drive the pumps may be esti- 
mated from the manufactuer's figures for their water rates and 
from the horse-power actually delivered. These remarks of course 
apply to steam pimips; where power pumps are installed, the 
energy may be considered in the list of costs. 

(g) Work of the Ammonia-pump. It is preferable to find the 
net horse-power output rather than the indicated horse-power. 
From the data required for the net horse-power and from the num- 
ber of pump displacements, the sHp may be calculated as in 
ordinary pumping-engine trials. 

The required formula for horse-power is 

XT ^u 144(Pi-P2)F 

Net horse-power =—33^^^^-, 

in which Pi and P2 are the gage pressures worked against in 
pounds per square inch (that is, of the generator and absorber, 
respectively) and V is the number of cubic feet of strong aqua 
circulated per minute. 



324 TESTING REFRIGERATION MACHINERY 64 

The quantity of strong aqua V may be determined in several 
ways. A specially calibrated meter may be used on the discharge 
side of the pump; the aqua may be measured in calibrated 
tanks on the suction side; or it may be calculated from the 
amount of anhydrous circulating or from the quantity of weak 
aqua, the concentrations being known. For this last method 
(see(i)). 

When a receiver is installed to supply the ammonia pump, it 
may be readily calibrated so that the volume contained, corre- 
sponding to any height of the liquid in the gage-glass, is known. 
Now, by cutting off the flow from the absorber into this receiver 
for a short interval, the rate, in cubic feet per minute, at which the 
strong aqua is pumped out, may be ascertained. If desired, two 
receivers may be arranged in parallel, thereby enabling contin- 
uous measurement. 

(h) Weight of Anhydrous NH3 Circulated per Minute. Vol- 
ume measurements may be made in the same way as described 
under (g) for strong aqua. To convert the volumetric results 
into weights, a temperature or pressure reading also should be 
obtained to find the density of the liquid from the tables of prop- 
erties of ammonia. When closely accurate results on the anhy- 
drous quantity rate are desired, a favorite method is by direct 
weighing. Two ammonia drums, arranged in parallel, are piped 
in the line betw^een the condenser and expansion valve, so that 
they can be filled and emptied alternately. These drums are set 
on platform scales, the connections to them being horizontal and 
sufficientl}^ long to deflect about J in. under a load at the end of 
about I lb. The drums and contents may then be weighed with- 
out sensible error. The increase of accuracy of this procedure 
probably does not justify the elaboration of the apparatus. 

It is useful to find the number of pounds of anhydrous per 
minute per ton of refrigerating effect and to compare this with 
the amount theoretically required as tabulated in handbooks or 
calculated from heat contents under prevaiHng conditions. 



64 



TESTING REFRIGERATION MACHINERY 



325 



(i) Concentration and Specific Gravity of the Aqua. The 
concentration of aqua ammonia is determinable from its specific 
gravity. Given a definite solution of ammonia in water, its spe- 





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0.86 0.67 066 0.69 0.90 0.91 0.9E 0.93 0.94 095 096 0.97 0.9d 
SPECIFIC GRAVITV 

Fig. 105. — Concentration of Aqua Ammonia at 60° F., and Density- 
Variation. 



cific gravity is fixed at any one temperature, say 60°. At any 
higher temperature the solution occupies more volume, owing to 
expansion, and therefore has a lower specific gravity, although the 
concentration remains the same. Or to put it another way, for 



326 TESTING REFRIGERATION MACHINERY 64 

any value of the specific gravity the concentration depends on 
the temperature. 

The chart, Fig. 1C5, gives values of the concentration of 60° 
aqua, corresponding to various specific gravities. 

Because of the volatility of aqua ammonia at the high tem- 
perature, and reduced pressure prevailing when a sample is drawn, 
considerable care must be taken when testing for concentration. 
The following procedure is recommended. Outlets for samples 
of the aqua are arranged at points where the temperatures are 
comparatively low; that is, on the discharge side of the pump 
for the strong aqua and between the absorber and weak-aqua 
cooler for the weak. These outlets should be fitted with short 
lengths of rubber tubing. A glass graduate, reading preferably 
in cubic centimeters, is provided, together with a hydrometer or 
a sensitive scales. The graduate is about half filled with water 
for the first trial (for the second, a somewhat different amount 
may be selected, depending upon the outcome of the first) and 
then placed in a bucket of cold brine until it and its contents are 
chilled to about 32°. . After running a little aqua through the 
sampling tube, it is directed below the surface of the water in the 
graduate until the mixture of cold water and incoming aqua 
attains a temperature of about 60° as shown by a thermometer. 
The specific gravity of the mixture should now be taken quickly 
with a hydrometer or by weighing the contents of the graduate 
and then by calculation. Provided the temperature is within 5 to 
10° of 60°, the concentration of the mixture may now be found on 
the chart. Fig. 105, against the determined value of its specific 
gravity. It is the concentration of the sample that is sought, 
however, and this may be calculated from the following relation: 

Cone, of sample = cone, of mixture -^ ( 1— — j, 

in which R is the ratio of the volume of cold water, before mixing 
with the sample, to the volume of the mixture, and Sm represents 
the specific gravity of the mixture. 



64 TESTING REFRIGERATION MACHINERY 327 

If scales instead of hydrometer are used to obtain the weights 
of cold water and mixture, then the concentration of the sample 
is more readily figured from the relation 

^ r 1 r ' J. ^, weight of mixture 

Cone. 01 sample = cone, oi mixture X e-j ^ 1— . 

weight 01 sample 

If the temperature of aqua ammonia is higher than 60°, its 
specific gravity will be lower by between 0.001 and 0.005 for each 
10°, depending upon the concentration, the stronger solutions 
having a higher coefficient of expansion and therefore needing 
greater correction than the weaker. Under these circumstances 
the specific gravity Sqo of a given solution at 60° can be figured 
from its specific gravity St at t^, the following formula, which 
gives moderately accurate results, being used :* 

SQo = St+0m3it-60)(l-Si). 

For example, if the specific gravity is found to be 0.865 at 75°, 
then at 60° it equals 

>S6o = 0.865+0.003(75-60)(l-0.865) -0.871. 

The value 0.871 is then to be referred to the chart for the cor- 
responding concentration. 

When the reverse calculation is sought (for the density deter- 
mination of aqua at high temperatures) this formula may be ex- 
pressed thus: 

aSgo- 0.003 (^-60) 



St = 



1-0.003(^-60) 



(j) Calculation of Aqua and Anhydrous Weights per Minute 
from the Concentrations. This method is based upon the follow- 
ing rational relations. 

* Curves presented in Marks' Mechanical Engineers' Handbook may also 
be used. 

t See also the equation and chart given under Test 65 (a). 



328 TESTING REFRIGERATION MACHINERY 64 



v^s ^t 



x^, 



i-a 



iij — ^j yr Xw4|/7, 



X-^s> 



A. = A.S AfD) 

in which As^ Aic and A are the weights in pounds per minute of 
the strong and weak aqua and anh3'drous respectively, and C, 
and C^ are the concentrations of the strong and weak aqua 
respectively, in pounds of NH3 per pound of solution. 

For direct measurement of these quantities, much the same 
methods may be employed as for the strong aqua. (See (g).) 
The reader is reminded that only one of the three quantities, 
Ay Au,, or As, need be directly measured for a fairly accurate 
knowledge of the performance of the plant when the concentra- 
tions are known. The ammonia, whether aqua or anh3'drous, 
may therefore be directly metered at a point selected according 
to the existing layout. It should be borne in mind, however, that 
the results depending upon concentration figures may not be exact, 
because of the difficulty in getting close values of the concentra- 
tions. 

It is to be noted that, since these relations are between weights, 
a knowledge of densities is necessary to convert them into or from 
volumes. For the aqua this involves a measurement of specific 
gravity; for the anhjTlrous the ammonia tables may be referred to. 
The chart, Fig. 105, gives values of the density of aqua corre- 
sponding to those of specific gravity, the density scale being on 
the right. 

As an example of how these relations are to be applied, let us 
suppose that the concentrations of the strong and weak aqua 
are 38, and 2G per cent respectively (the concentrations having 



65 TESTING REFRIGERATION MACHINERY 329 

been found as under (z)), and that the number of pounds of anhy- 
drous circulated per minute is 20. Then. 



A,= 



^-TTz — '-z-^-X20 = 123 lbs. per minute. 
0.38 — 0.26 



Referring to the chart, it is seen that 38 per cent aqua has a 
specific gravity of 0.873, if the aqua is at 60° F., and a density of 
54.4 lbs. per cu. ft. 

For the calculation of (gf), if the temperature of the aqua 
at the pump is not much higher than this, then the cubic feet dis- 
charged per minute is 123-^54.4 = 2.26, which is the value of V 
to be used in the formula for horse-power. 

65. Heat Balance of a Refrigeration Plant 

(Ammonia Absorption System) 

Principles. The over-all heat transfers in an absorption 
refrigeration plant may be summarized very briefly as follows: 
Energy is added to the system, first by the steam supplied to the 
generator, second by the work of the ammonia pump, and third 
by the heat added to the brine during the refrigerating process. 
Heat is removed from the system by circulating water, first in the 
ammonia condenser, second in the absorber, and lastly, in the 
weak-aqua cooler and the rectifier. The energy added equals the 
heat removed, as itemized, plus or minus radiation. 

A study of this over-all heat balance is useful, but before 
making comparisons of grand totals, it is preferable to analyze 
the performance of separate units. Of these it is the purpose 
here to deal with the generator and the absorber. 

To review the action of the generator, strong aqua ammonia 
enters at a comparatively low temperature, to which heat is added 
by steam pipes. Some of the ammonia is thereby boiled out of 
the water holding it in solution. There result from the process a 
quantity of superheated anhydrous ammonia, mixed with a small 



330 TESTING REFRIGERATION IMACHINERY 65 

percentage of steam, and a larger quantity of weak aqua, com- 
paratively hot, which is to be retm^ned to the absorber. The 
heat in the steam supplied goes to vaporize and superheat ammonia 
from the form of strong aqua and to raise the temperature of the 
entering aqua to a higher value upon leaving. Furthermore, a 
certain quantity of heat is required to break the bond between the 
hquid ammonia and the water holding it in solution, before vrpor- 
ization can take place. This quantity is additional to that re- 
quired to vaporize liquid anhydrous ammonia and is referred to as 
the " heat of solution.'^ Experimental values of it have been 
made showing that it is independent of pressure and temperature 
and varies only with the concentration of the solution, being about 
347 B.t.u. per pound for very weak solutions (approximately to 
zero percentage of ammonia) and diminishing as the concentra- 
tion is increased to a zero value when the concentration is 60 per 
cent. 

It is convenient to base the heat calculations of the ammonia 
upon a single pound of the NH3 going through a complete cycle of 
temperature and state changes. From these results hourly quan- 
tities may be figured by multiplying by the number of pounds of 
anhydrous circulated per hour. Thus, let A represent the latter 
quantity and W the number of pounds of weak aqua circulated 
per pound of anhydrous vaporized; then the heat transfer '^d in 
the generator per hour = ^ X(Trxheat added to 1 lb. of the 
aqua+heat of solution in B.t.u. per pound of NH3 + difference in 
^' heat content '^ of NH3 per pound, from tables). The quantity 
in the parenthesis is the heat transferred for the circulation of one 
pound of the anhydrous. 

The product, representing B.t.u. per hour, must equal the heat 
given up by the steam supplied to the generator, if the losses due 
to radiation and steam in the superheated ammonia are ignored. 

The Measurements Necessary to make for the determination of 
this heat balance are in part the same as those for an economy 
trial, for which see Test 64. In addition it is necessary to deter- 



"'^^ 



65 TESTING REFRIGERATION MACHINERY 331 

mine temperatures of the ingoing and outgoing aqua near the 
generator, the temperature of the ammonia vapor before it enters 
the rectifier and the head pressure — readings of which should be 
taken sufficiently to get fair averages. The vapor data are used 
to determine the ^^ heat content '^ from the tables (see Appendix), 
or Mollier diagram for ammonia. For the steam-heat quantities, 
pressure and quality must be ascertained as well as the tempera- 
ture of the condensate at the generator tiup. 

(a) To determine the number of pounds of weak aqua cir- 
culated per pound of anhydrous (that is, IF), it is necessary to 
measure the concentrations of the weak and strong aqua (referred 
to as Cto and C^, respectively) as described under Test 64 (z). 
The desired quantity may then be calculated from the rational 
formula, 

TIT ^W -I ^a 



Ji. L/5 i^n} 



A simpler procedure may be adopted through the use of the 
accompanying curves. Referring to Fig. 106, the lines slanting 
diagonally upward from left to right show values of the number 
of pounds of weak aqua per pound of anhydrous corresponding to 
various combinations of concentrations. To use these curves 
assume, for example, that the concentration of the strong aqua 
is 0.34, and of the weak, 0.24. On the chart the lines representing 
these values intersect between the curves marked 6.5 and 7, at 
about one-fifth of the distance across, so the value of W is 6.6. 

This chart also gives the ^' heat of solution,'^ which is plotted 
from the experimental values of H. Molher. As previously 
remarked, this depends only upon the concentration. During 
the driving-off process in the generator, the concentration varies 
from that of the strong aqua to that of the weak. It is the average 
concentration, then, that determines the heat of solution. This 
condition is met in the chart, as before, by the intersection of the 
lines representing the concentrations; the location of this point 



332 



TESTING REFRIGERATION MACHINERY 



65 



with relation to the ''heat Knes " (slanting downward from left 
to right) gives the heat of solution. For example, using the 
concentrations 0.34 and 0.24, the point of intersection is about 
four-fifths of the distance across from the 205 to the 210 B.t.u. 
line. Therefore the heat of solution is 209 B.t.u. 




Q20 02\ 022 0.23 024 025 026 027 028 029 030 0.31 052 033 0.34 0.35 0.36 037 0.38 0.39 0,40 
Concentrotion of strong Aqua 

Fig. 106. — Heat of Solution of Aqua Ammonia 

(b) Heat Added to NH3 and Aqua in Generator. We no\A 
have means of finding the number of pounds of weak aqua pci 
pound of ammonia vaporized and the heat of solution per pound, 
Referring to the heat equation for the generator, already given, ii 
will be noticed that there are still to be found the heat added t' 
one pound of the weak aqua and the difference in ^^ heat content 'I 
of the NH3 before and after vaporization. The latter is readihj 
found from the ammonia tables or ]\Iollier diagram, being thi 
difference between the total heat of the NH3 vapor at the heacj 
pressure and outgoing temperature and the heat of the liquici 
NH3 at the temperature of the incoming strong aqua. 



65 



TESTING REFRIGERATION MACHINERY 



333 



Considering, now, the heat added to one pound of the aqua 
passing through the generator, it is to be remarked that there are 
no tabulated values of the heat of the liquid of mixtures of ammo- 
nia and water, or of the specific heats of such mixtures. It will, 
however, be sufficiently accurate to assume that the heat capacity 



210 
200 
190 
180 
170 
160 

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50 eO 70 80 90 100 110 leo 130 140 160 160 170 180 190 200 
Temperature, Degrees Fahrenheit 

Fig. 107.— Heat of the Liquid for Water, Aqua Ammonia and Anhydrous 

Ammonia 



of a combination of ammonia and water in definite proportion is 
the sum of the heat capacities of the constituents, according to 
their proportion. Thus, if we call the heat of the liquid of ammo- 
nia ha and of the water, K (as tabulated in the ammonia and steam 
tables, respectively), then for a mixture of C pounds of ammonia 
and 1-C lb. of water, the heat of the liquid (aqua ammonia) = 
/iaC+/z^(l-C). Values of this quantity at various temperatures 



334 TESTING REFRIGERATION ?^IACHINERY 65 

and concentrations are shown graphically in Fig. 107, the highest 
curve of which gives (vertically) the heat of the liquid of pure 
ammonia, the lowest curve, of unmixed water, and the inter- 
mediate curves, of mixtures of the two denoted by their con- 
centrations. The heat of the liquid of aqua at concentrations 
intermediate between those shown may be obtained with sufficient 
accuracy by interpolation. 

Coming now to detailed calculations, let us assume the fol- 
lowing data: 

Concentration, weak aqua, Cm? = 0.24. 
Concentration, strong aqua, (75 = 0.34. 
Head pressure = 100.3 lb., gage. 
Temperature of outgoing NH3 = 150° F. 
Temperature weak aqua = 180° F. 
Temperature strong aqua = 130"^ F. 

From Fig. 106 is obtained the value 6.6 as the number of pounds 
of weak aqua leaving the generator per pound of ammonia vapor- 
ized. From Fig. 107 the heat of the hquid of one pound of 24 per 
cent aqua is found to be 158 B.t.u. at 180"^ and 102B.t.u. at 130^ 
Consequentl}^, the heat added to the aqua per pound of ammonia 
vaporized is 6.6X(158-102) =370 B.t.u. From Fig. 1C6, from 
the given concentrations, heat of solution = 209 B.t.u. From the 
ammonia tables, the total heat of ammonia at 100.3 lbs. gage and 
150° is 609 B.t.u., and the heat of liquid ammonia at 130° (its 
incoming temperature) is 115 B.t.u. (also obtainable from Fig. 107). 
The heat added to the NH3 to raise it from the liquid to the super- 
heated condition is consequently 609 — 115 = 494 B.t.u. Adding 
these three heat quantities (370+209+494 = 1073 B.t.u.), we 
have the heat added in the generator to effect the complete cir- 
culation through the plant of one pound of anh3^drous ammonia. 
As before mentioned, this ignores the loss through vaporization of 
water with the ammonia, afterward removed by the rectifier, 
but this loss should be small. 



65 TESTING REFRIGERATION MACHINERY 335 

(c) The Steam-heat Quantities involve the determination 
of the weight of steam used for a corresponding ammonia vapor- 
ization and may be made as for an economy trial. (See Test 64 
(e)). It should be noted that 

^ , ^ , heat added to NH3 and aqua per hour 

Lb. of steam per hour = — r — 7 -j-? rri: — t~i • 

heat removed irom 1 lb. 01 steam 

(d) The Heat Transfers in the Absorber are essentially the 
same as in the generator, the only difference being that they 
proceed from the ammonia media into circulating water, instead 
of from steam into ammonia media, and heat is given up, instead 
of taken in, by the NH3 and aqua. The aqua is pumped from the 
absorber at a temperature lower than that at which it entered, 
whereas in the generator the reverse was the case. The heat of 
solution is released in the absorber and must be removed by the 
circulating water, also a reverse process. The anhydrous vapor, 
coming from the refrigerator at comparatively low pressure, is, 
taken into solution by the weak aqua, consequently giving up 
(in addition to the heat of solution) an amount equal to the total 
heat of the incoming anhydrous minus the heat of the liquid NH3 
at the temperature of the outgoing (strong) aqua. It will thus 
be seen that the measurements and calculations for the deter- 
mination of the heat given up by the absorber per pound of anhy- 
drous ammonia are exactly the same as for the generator. 

(e) Heat Removed by Condenser Water. The heat calcu- 
lated under (d) expressed in B.t.u. per unit of time, equals the heat 
removed from the circulating water in the same time, plus or 
minus radiation. To obtain the heat removed, it is necessary 
to measure the circulating water for a definite time, as for an 
economy trial, and its temperature range between entering and 
leaving the absorber. (See Test 63 (g)). 



336 TESTING OF AIR MACHINERY 66 



66. Test of a Fan Blower 

Principles. There are two kinds of fan blowers called 
^' pressure '^ and '^ volume''; the one delivering air at high pres- 
sure, the other at high velocity. The shape of the fan casing to 
a large extent determines its kind. 

The capacity of a blower depends upon the volume of '^ free 
air '' it will discharge in a given time at a given rotative speed. 
By free air is meant air at the pressure and temperature of the 
room at the time of the test. Capacity is generally expressed 
in cubic feet per minute. 

The useful work done by a fan equals the energy imparted 
to the air as pressure and velocit3^ If W is the number of pounds 
of air discharged per minute, and Hi is the pressure expressed 
as a head of air in feet, then WHi is the foot-pounds of useful 
work per minute represented by the pressure energy. If V is 
the velocity in feet per second, then TrF^-^64.4 is the foot-pounds 
of useful work represented by the kinetic energy. The quantity 
r--^64.4 is the head of air, in feet, equivalent to the velocity, 
or " velocity head,'' which will be referred to as H. Then the 
useful, or ^^ air horse-power," is 

WHi + WH 
^•^'•P-~ 33,000 • 

This is referred to by the Air Machinery Code of the A.S.M.E. 
as the ^' gross " air horse-power; the difference between it and 
the '' uet " will be pointed out under Test 67. 

Selection of the Independent Variable. In the operation 
of a fan blower, either the rotative speed, the velocity of air, 
or the pressure of the air may be varied. The first is controlled 
according to the type of the driving engine. The air velocity 
or pressure may be varied at a given rotative speed only by 
changing the size of the outlet from the air discharge pipe. A 



66 TESTING OF AIR MACHINERY 337 

useful set of tests may be had by making the rotative speed the 
independent variable. The pressure is kept constant during 
a series of runs at different speeds; then the pressure is changed 
for another series, and so on. In order to keep the pressure 
constant when the speed is changed during each series, it is 
necessary to adjust the external resistance to the air. This 
may be done by using different nozzles or orifices as outlets 
from the discharge pipe. A convenient arrangement consists 
of a leaf shutter, similar to that of a camera, which may be 
readily changed to any desired diameter of outlet orifice. 

A set of curves may be made between the various results and 
the rotative speeds. For each pressure there will be a corre- 
sponding set of curves. Taking the results from these curves 
on a coordinate representing one value of the speed, another 
set of curves may be plotted with pressure as the independent 
variable. A number of such sets may be made corresponding 
to various speeds. 

Another independent variable which is sometimes used is the 
size of the orifice or nozzle in the outlet pipe. Pressure and 
velocity will then vary at each different speed, and these with 
the other variables may be plotted against orifice area; one set 
of curves for each speed of the blower. 

The duration of each run need not be more than a few minutes 
if a velocity meter is used for air measurement. The observed 
quantities vary very slightly, as a rule, during each run, so that 
only two or three sets of observations are needed. 

(a) Determination of Horse-power Supplied. If the fan is 
belt driven, a transmission dynamometer ma}^ be used to advan- 
tage. Allow^ance should be made for belt losses, since the horse- 
power supplied to the fan shaft is desired. This may be done 
by using the revolutions per minute of the fan shaft with the 
torque shown by the dynamometer to calculate horse-power, 
and multiplying the result by the ratio of diameters of fan pulley 
to dynamometer pulley. This allows for belt slip. 



338 TESTING OF AIR MACHINERY 66 

If the fan is driven by an electric motor, the horse-power 
supphed may be had from a cahbration of the motor, readings 
of the current supphed then being necessary. 

(b) Capacity. For the measurement of the air quantity a 
meter of the velocity type is most readily adapted. Of these, 
anemometers (Test 28), orifices (Test 27), and pitot tubes (Test 
25) are customarily used, preference being given to pitot tubes. 

Velocities may be obtained from the pitot tube either by 
making a complete traverse of the pipe at each determination, 
or by locating the velocity opening at the point of mean velocity. 
For details, see Test 25 (a). ]\Iultiplying the velocities by the 
cross-sectional area of the pipe gives volumes of air under the 
pipe conditions of pressure and temperature. To reduce these 
results to free air, pressures and temperatures of the air in the pipe 
and room must be read. In the pipe, the pressure may be read 
from a manometer attached to a branch from the tube leading 
to the static opening of the pitot meter. For room pressure, 
the barometer should be read. 

Consider as an example the following readings. Velocity 
head, /z = 0.5 in. of water; pressure = 4 ins. of water; barometer = 
29.9 ins. of mercury; temperature of room = 65° F.; tempera- 
ture of air in pipe = 67° F. The absolute pressure of the air 
in the pipe is 29.9+4-^13.6 = 30.2 ins. of mercury or 30.2X0.49 
= 14.8 lbs. per square inch. 

The absolute temperatures of the room and of the air in the 
pipe are 525° and 527°, respectively. The density of the air 
in the pipe may be figured from the familiar relation, 

53.47^ r 

which gives w; = 2.7X14.8-^527 = 0.0758 lb. per cubic foot. 
To convert the velocity head />, in inches of water, into //, in 
feet of air, we have, 



66 TESTING OF AIR MACHINERY 339 

for the given data. Consequently, // = 68.5X0.5 = 34.25, and the ' 
velocity is 

7 = 8.02VF 

7 = S.02V34.25 = 47 ft. per second. 

If the area of the pipe is 0.33 sq. ft., the cubic feet of air per 
minute is 60X0.33X47 = 930. To reduce this to free air, it is 
multiplied by the ratio of temperatures and the inverse ratio of 
pressures. 

525 30 2 
Free air per minute = 930X37^X7^777^ = 934 cu. ft. 

527 29.9 

(c) Horse-power Supplied per Thousand Cubic Feet of Free 
Air per Minute. This quantity is obtained from the results of 
(a) and (b) being the quotient between each two corresponding 
values multiphed by 1000. 

(d) Air Horse-power. For the data previously given, the 
weight of air delivered per minute is 930X0.0758 = 70.5 lbs. 
The velocity head is 34.25 ft. of air, and the pressure head, 
68.5X4 = 274 feet of air. Then the air horse-power is 

. , 70.5(34.25+274) „ ._^ 
A.h.p. = 33^^^^ = 0.659. 

(e) The Efficiency equals the air horse-power divided by the 
horse-power supplied. 

Problem 661. In the test of a blower, if gasoline, specific gravity =0.75, 
is used as a gaging fluid with a pitot tube, what is the velocity head in feet 
of air, if /i=4.5? Pressure is 6 ins. of the same fluid. Barometer is 30.3 
ins. mercury. Temperature is 70° F. Ans.j 229 ft. 

Problem 662. In the preceding how many foot-pounds of work will be 
done in one minute if pipe dia. =6 in.? Ans., 58100. 



340 TESTING OF AIR MACHINERY 67 

Problem 663. In the operation of a blower, the volume discharged varies 
very nearly as the rotative speed. The pressure is due to centrifugal force. 
From these facts, deduce how the power will vary with the speed. 



67. Test of a Reciprocating Air Compressor 

Principles. In the operation of an air compressor, it is the 
purpose to increase the pressure of the air suppHed so as to make 
available the energy it contains. As this energy is to be used 
when the air is cool, it is desirable to compress the air isothermally. 
If it is allowed to heat, the pressures during compression are 
higher and more work is required for compression. For this 
reason, w^ater jackets and intercoolers are used, the heat removed 
by them being a saving. 

Referring to Fig. 108, the dotted lines show an ideal air com- 
pressor diagram from a cylinder without clearance in w^hich the 

air is discharged at a pressure, 
42 — 5i, equal to that in the de- 



5".T — 4}\\^ Inlet Valve Opens at 1 Hvcry main. The supply is 

%%^55u?e ^A "^ ^^^'^^ " ^P^^""^^ " ^ drawn in at atmospheric pres- 
v\ - '> 0363 ' ^^^^ along the line 61 — 2i and 

°'*<J^'%^ then compressed isothermally 

"VS^".^ along 2i-42. 

), T r ' y^^ l' I he actual mdicator diagram 

1 varies from the ideal one as 

Fig. 108.— Ideal and Actual Air shown by the full lines, 1-2-4-5. 
Compressor Diagrams. The friction resisting the motion 

of the air through inlet and 
outlet valves and ports necessitates a lesser pressure than 
atmospheric to draw in the air, and a greater pressure than that 
in the delivery main to discharge it. Consequently, work is 
lost as represented by the areas 4-5i-5 and 1-2-3-6. The actual 
compression line, 2-4, must be above isothermal because of the 
impossibility of perfect cooling, and this results in the loss rep- 



67 TESTING OF AIR MACHINERY ^ 341 

resented by the area between the Hnes 2-4 and 2-4i. These 
are '^ compression '^ losses. 

When the outlet valve closes at point 5, an amount of air 
equal to the clearance volum.e is entrained in the cylinder. At 
the beginning of a new cycle, this air expands so that the effective 
stroke for drawing in air begins at point 6 instead of 6i. This 
point occurs later, the higher is the delivery pressure (at 5). 
When the inlet valve closes at 2, the air in the cylinder is rarified 
because of the suction, and it is not until 3 is reached that its 
pressure becomes atmospheric. The effective stroke for drawing 
in air is therefore represented by line 6-3 instead of the full length 
of the diagram. This is a ^' volumetric ^^ loss, since less air is 
delivered than would be if the full stroke were effective. Another 
volumetric loss, not appearing in the diagram, is due to leaky 
valves and pistons, similar to slip of a pump. 

After the air in the delivery pipe has been cooled down to 
room temperature, it contains energy, due to its pressure above 
atmospheric, available for performing work. If this air could 
be expanded isothermally to its original pressure, there could be 
regained all of the energy necessary to compress it isothermally. 
This, however, cannot be done, the actual expansion being more 
nearly adiabatic. There is a final loss, then, due to the lack of 
availability of all the energy added to the air. 

These various losses are indicated in certain expressions for 
efficiency, to be defined in the following, which are generally 
figured as air compressor test results. It is first necessary to 
define : 

Gross Air Horse-power. This is the same as the indicated 
horse-power of a steam engine, being figured from the mean 
effective pressures of the indicator diagrams of the air cylinders. 

Net Air Horse-power. This is the horse-power required to 
compress isothermally from room pressure and temperature 
to the pressure in the delivery main, a mass of air equal to that 
actually delivered. 



342 TESTING OF AIR MACHINERY 67 

The Mechanical Efficiency equals the gross air horse-power 
divided by the horse-power supplied to the compressor. 

The Volumetric Efficiency is the cubic feet of free air actually 
delivered in a given time divided by the low pressure piston dis- 
placement in the same time. 

The Efficiency of Compression is the net air horse-power 
divided by the gross air horse-power. This efficiency covers 
all the losses of the air cylinders due to faulty valve action, leak- 
age, lack of cooling, etc., except that due to mechanical friction. 

Over-all Efficiency is the net air horse-power divided by the 
horse-power available for running the compressor. 

(a) Capacity may be expressed as the number of cubic feet 
of air discharged per minute at the pressure in the delivery main 
corrected to room temperature, or as the number of cubic feet 
discharged per minute reduced to free air, that is, air of the same 
temperature and pressure as that supplied to the compressor. 

Let (3 = cubic feet of air per minute discharged, as found by 
meter; 
7" = absolute temperature, degrees Fahrenheit of air dis- 
charged; 
P = absolute pressure, pounds per square inch, air dis- 
charged; 
^ = absolute temperature, degrees Fahrenheit, of air 

supplied (room); 
p = absolute pressure, pounds per square inch, air supplied. 

Then the capacity in terms of compressed air is 
and in terms of free air is 

^3 = Qx|x^=QiX^. 



67 TESTING OF AIR MACHINERY 343 

T and t are to be determined by thermometers, one in the room 
near the air inlet to the compressor; the other in the discharge 
pipe just beyond the last cylinder or receiver, p is obtained 
by a barometer and reduced to pounds per square inch; P, 
by a pressure gage set close to the thermometer measuring T, 

The cubic feet of air Q flowing in the dehvery main is a quan- 
tity difficult to measure accurately. The methods outlined 
under Part I are applicable, but, owing to the high pressures 
and large volumes, are not altogether satisfactory. Gasometers 
give the most reliable results. Two tanks similar to Fig. 56 
may be connected together at the bottoms by a water pipe, 
and air piping arranged so that they may be alternately filled 
with the discharge from the compressor. As air enters one, 
water is displaced into the other until a mark on the gage glass 
is reached. The air is then diverted into the other tank, the 
water returning to the first one which at the same time discharges 
the air it has just been filled with. The cross-sectional area 
of the tanks and the distance between upper and lower water 
levels, together with the number of fiUings per minute, give the 
quantity sought. It is a good plan to pipe the air through a 
four-way cock so arranged that one motion connects one tank 
with the air delivery line and the other tank with the atmos- 
phere. 

(b) Mechanical Efficiency. The gross air horse-power is 
figured from the indicator diagrams from the air cylinders. The 
horse-power supplied to the air compressor, if it is steam driven, 
is the indicated horse-power of the steam cylinders. If it is 
belted or geared to the source of power, the horse-power supplied 
is that received at the compressor shaft, and should be obtained 
as for a fan blower, Test 6 3 (a) . From these results the mechanical 
efficiency may be obtained. 

(c) Volumetric Efficiency. The length of the line 6-3, Fig. 
108, divided by the length of the diagram 6i-2i, is often referred 
to as the ^^ apparent ^^ volumetric efficiency; apparent, because 



344 TESTING OF AIR MACHINERY 67 

it does not take account of slip and leakage. The ^^ true 'Volu- 
metric efficiency is, 

in which L is the length of the stroke in feet, An and Ap are the 
areas in square feet of the piston at the head and power ends, 
respectively, and N is the number of double strokes per minute. 
If the compressor is single-acting, Ap should be omitted. 

If the compressor has more than one cylinder, the expression 
applies to the low-pressure cylinder. 

(d) EflSciency of Compression. The net air horse-power 
must first be figured. The work done during isothermal com- 
pression of a gas is mathematically equal to 

, V. 1 v.T 11-1 final abs. pressure 

abs. pressure X volume X hyperbolic log. . .^. , — \ — . 

mitial abs. pressure 

The volume to be considered in this case is that accounted for in 
the delivery main, corrected to room temperature. Then, using 
the notation given under (a), 

144PQi log.;^ 
NetA.h.p.^ 33,000 '' • 

Dividing this by the gross air horse-power gives the required 
result. 

(e) Over-all Efficiency. The horse-power available for running 
the compressor, in the case of a belted or similar machine, is 
the horse-power supplied to the shaft, the same as the denominator 
of the fraction expressing mechanical efficienc3\ For a steam 
driven machine, it is the horse-power available in the steam 
supplied. This may be taken as the horse-power that would 
be developed if the steam worked on the ideal Clausius cycle. 



67 



TESTING OF AIR MACHINERY 



345 



If Ec is the Clausius cylinder efficiency, figured according to 
Test 45 (c), then 

H.p. available in steam = I.h.p. in steam cylinder -^£'c. 

Dividing the available horse-power into the net A.h.p. gives 
the over-all efficiency. 

(f) Separation of Losses. A precise separation of all the 
losses cannot readily be made for the reason that they merge 
into each other. For example, mechanical friction in the air 
cylinder adds heat to the air which m.akes the loss due to inef- 
fective cooling greater. If there is leakage of air past the inlet 
valve during the compression, the compression curve will approach 
more nearly to the isothermal, making an apparent gain in the 
jacket^s efficiency, but an actual loss as far as power and capacity 
are concerned. Again, if the inlet valve is mechanically operated 
and opens too early, the compressed air in the clearance space 
escapes and the apparent volumetric efficiency is improved, 
but power is lost. 

If it is borne in mind that the losses as shown by the indicator 
diagram are not precise, an idea may be formed of them by an 
analysis of a representative 
diagram from a test. Fig. ^ r f 4 
109 is such a one. Through 
2i, vertically over 2, a 
horizontal should be drawn 
to represent atmospheric 
pressure. Through 2i an 
isothermal is drawn referred 
to a volume axis through 5. 
Through 2, another iso- 
thermal is drawn referred 
to the volume axis OY, 

located from the left of the diagram at a distance proportional 
to the clearance of the cylinder. Finally, a horizontal through 




Fig. 109. — Air Compressor Losses. 



846 TESTING OF AIR MACHINERY 67 

42 is laid off to represent the pressure in the delivery main. 
The ideal diagram is then 6i-2i-42-5i. 

The loss due to fluid friction at the valves and ports is 
represented by areas /, /. 

The los-s due to insufficient cooling by the jacket water is 
represented by area j. 

The loss in capacity due to volumetric inefficiency other 
than leakage is represented by the areas c, c. This is not a 
loss of power supplied, since the work is not done. It is merely 
a diminution of the capacity of the compressor to deliver net 
horse-power. 

The loss in capacity due to leakage is also a loss of power, 
because work is done on the air which leaks out of the system 
just as it is done on that which is discharged into the delivery 
main. To estimate this loss, a point 2o, Fig. 109, is located 
so that the distance 6i-2o = distance 6i-2iXtrue volumetric 
efficiency. Through 2o an isothermal is drawn referred to 5-6i 
as the volume axis. The diagram 6i -2o-4o-5i then represents the 
net horse-power, and the area v, the loss of power due to leakage. 

These areas may be integrated and expressed as per cents 
of the area representing the gross horse-power. 

If the compressor has more than one cylinder, the indicator 
diagrams should be combined by reconstructing them on the same 
scale. The line 42-5i will then represent the receiver pressure. 
The next cylinder diagram will have this line as a datum in the 
same wa}^ that the low-pressure cj'linder diagram has the 
atmospheric hne as a datum. The general method outlined in 
Test 46 (/) may be used for construction. 

(g) Heat Measurements. The heat equivalent of the work 
delivered to the air piston 

= heat added to the jacket water 

+heat in the air in delivery main, above room 

temperature 
+heat radiated. 



67 TESTING OF AIR MACHINERY 347 

This follows from the fact that no energy is added to air when 
it is compressed, or expanded, isothermally, the isothermal being 
a ^^ constant energy '^ condition. The heat removed per minute 
by the cooling water may be measured by taking weight and 
thermometer readings. The heat in the air may be figured from 
the data for the other results and from the specific heat of air. 
These quantities, considered with regard to the other results, 
will give a more complete idea of the efficiency of cooling. They 
may be expressed in horse-power units by dividing by the 
number of heat units per minute equivalent to one horse-power, 
42.42. 

Problem 67i. An air compressor delivers 8.3 cu. ft. of air per minute, 
at 100 lbs. pressure absolute, and 220° F. What is its capacity in cubic 
feet of free air per minute; temperature of the room being 75°, and pressure, 
29.5 ins. of mercury? What is its capacity in cubic feet of compressed air 
corrected to room temperature? Ans.f 45.1 and 6.52 cu. ft. 

Problem 672. The compressor of the preceding problem was two-stage^ 
14-in. and 9-in. bore by 12-in. stroke, and 100 working strokes per min. 
per cylinder. What is the volumetric efficiency from the same data? 

Ans,, 42.2%. 

Problem CTs. What is the net air horse-power from data of Problem 
67i? What is the horse-power available in the compressed, cooled air? 

Ans.y 5.5 H.p. 

Problem 674. How can the area jj Fig. 109, be roughly figured from heat 
measurements? 



68. Test of a Hydraulic Tuebine 

Principles. The horse-power dehvered by a hydrauhc tur- 
bine is as indicated by a dynamometer apphed to its shaft. The 
horse-power available is that of the water which drives it, and 
is proportional to the difference in level between the head race 
and tail race, and the weight of water flowing per minute. The 
quotient between these horse-powers equals the over-all efficiency 
of the plant. 

When the turbine is supplied from a pipe line under pressure, 
as in the arrangement of wheels of the Pelton type without a 



348 TESTING OF WATER MOTORS 68 

draft tube, the horse-power available to the machine may be 
taken as that due to the pressure and velocity energy of the 
water just before entering the turbine. The machine is then 
not charged with the friction losses of the pipe line or with the 
losses due to its position in relation to the tail race. 

Selection of the Independent Variable. In operation, any 
or all of the following may be varied. First, gate or needle valve 
opening; second, rotative speed; and third, brake horse-power. 
For test purposes, the head on the turbine may also be varied. 

Change of the gate opening varies the amount of water sup- 
plied. Change of the brake horse-power is accompanied by 
a change of speed if the gate opening is left the same. 

Laboratory tests are usually made at a constant head. The 
gate is adjusted at a predetermined opening for one series of tests. 
Then, by regulating the brake, the speed is varied for this series, 
and data obtained at each speed. Another series of tests is then 
made at a different gate opening, and so on until the full range 
has been covered. 

If it is desired to test the performance at different heads, 
all or part of the above tests may be repeated after changing the 
head. 

It is useful to plot brake horse-power and efficienc}^ at each 
gate opening against speed. 

The duration of each run need be only long enough to obtain 
accurate measurement of the rate of water supphed when the 
head remains practically constant, once uniformity of conditions 
has been established. 

(a) Available Horse-power. This equals 



or 



33,000 33,000 



in which W is the weight of water per minute in pounds; H, 
the difference in level in feet, for the first case; and for the 



68 TESTING OF WATER MOTORS 349 

second, p is the pressure in the water pipe in pounds per square 
inch; V, the velocity in feet per second, and g the acceleration 
of gravity. 

It should be noted that the first expression is the energy 
available to the turbine plant, the second is the energy available 
to the turbine. 

The most convenient method of measuring the water supplied 
is by weirs, the quantity usually being large. For small turbines, 
calibrated tanks may be used instead. 

' When the difference of level between the head race and tail 
race is measured, two datum marks may be made at the 
approximate positions of the upper and lower levels. The 
variations of the levels from these marks may be noted at a 
number of time intervals during each run. From these data, 
the average head available to the turbine plant ma}^ be figured, 
the vertical distance between the marks having previously been 
m.easured. 

When the second relation for available horse-power is used, 
the pressure may be obtained by a pressure gage just back of the 
control valve. The velocity is readily obtained from the pre- 
viously measured water quantity, the cross-sectional area of the 
pipe being known. Sometimes the velocity energy is small 
enough to be negligible. 

(b) Hydraulic Efficiency is obtained by dividing the horse- 
power available to the turbine into the brake horse-power. 
The latter may be measured by one of the forms of friction 
brake. 

(c) Determination of Best Operating Speed. The curve 
of efficiency vs. speed is something like an inverted U. The 
speed at the highest point of this curve gives maximum efficienc3^ 
It is approximately that speed which gives a peripheral velocity 
of one-half that of the jet for impulse wheels. For other types, 
it depends upon the characteristics of the turbines. 

Under ideal conditions, the water upon leaving the turbine 



350 



TESTING OF WATER MOTORS 



69 



vanes would have no velocity except that due to the acceleration 
of gravity, since velocity of the off-flow means lost energy. 
With some types of turbine the best speed may be ascertained 
by watching the off-flow and determining that speed which is 
accompanied by the most nearly vertical descent of the water 
as observed by the eye. 

Problem 681. What is the pressure energy- in foot-pounds per minute 
available to a Pelton wheel supphed with 10 cu. ft. of water per minute at 
100 lbs. pressure? Ans., 144,000 ft.-lbs. 

Problem 682. In the preceding problem, if the pipe supplying the water 
is 2 ins. inside diameter, what is the velocity energy? What is the total 
horse-power? Ans., 565 ft.-lbs. per min.; 4.38 H.p. 



69. Test of a Hydraulic Ram 

Principles. The hydrauhc ram is a pump wliich uses the 
energy of a large volume of water under a low head in order to 
deliver a part of the water at an increased head. This is ac 

complished by establishing a flow 
through a waste valve at the foo 
of the supply pipe. When the ve- 
locity thus started attains a certain 
value, it closes the waste valve 
whereupon the kinetic energy of the 
previously moving column in the 
supph' pipe is con\'erted into pres- 
sure great enough to open a valv 
into the discharge pipe. Water is 
then delivered at the increasec 
pressure until the pressure energy 
is reduced to the static condition 
when the discharge valve closes, th( 
waste valve opens, and the cycle recommences. Fig. 110 show.^ 
diagrammatically the arrangement of piping of a hydraulic ram 




IVcfs^ Wafer- ■•■>{ 



Fig. 110.— Hydraulic Ram. 



69 TESTING OF WATER MOTORS 351 

Two values for the useful work of a ram may be obtained, 
depending upon the level from w^hich the head pum_ped against 
is dated. Referred to the level of the supply water, the useful 
work is that corresponding to the elevation of a weight of water 
through the distance H, Fig. 110. Referred to the level of the 
ram, it is the work performed in lifting the same weight of water 
through the distance Ha- The one result leads to what is 
known as Rankine's efficiency, the other to D^Aubisson's. 
No confusion should arise through the existence of the two 
different efficiencies. Whether the one or the other should be 
used depends upon w^hether one is interested in pumping water 
from the supply level or from the level of the ram. 

Selection of the Independent Variable. Laboratory tests 
are generally conducted under a constant supply head, although 
this may be varied in the same way as for the test of a water 
turbine. If the supply head is maintained constant, either the 
number of strokes per minute of the waste valve or the discharge 
head may be made the independent variable. 

(a) Capacity is expressed in gallons of water pumped per 
tw^enty-four hours. This may be measured b}^ catching the 
discharge in a pail, or larger vessel if necessary, during a counted 
time. Instead of pumping against a static head as in regular 
operation, the discharge may be throttled by means of a valve 
in the discharge pipe which may then be short enough to collect 
conveniently the water delivered. The desired head is ascer- 
tained and regulated by the aid of a pressure gage between the 
ram and the throttle valve. 

If the number of strokes per minute of the waste valve is the 
independent variable, it can be varied by changing the lift of 
the valve, or adjusting the spring tension if it is operated by 
a spring. 

(b) Efficiencies. Let W and H stand for the weight of 
water flowing per minute in pounds and head in feet, respectively; 
and let the subscripts 5, w, and d refer to the supply, Avaste, 



352 TESTING OF WATER IMOTORS 69 

and discharge, respectively, as indicated by Fig. 110. According 
to Rankine's efficiency a weight of water Ww must fall Hs ft. 
in order to raise Wa lbs. of water H ft. Therefore, 

Rankine's efficiency = 



W^H, 



According to D'Aubisson's efficiency, the energy available 
to the ram is the denominator of the following expression, and 
this energy accomplishes Wa Ha ft-lbs. of work. 

D'Aubisson's efficiency = , . 

Wstls 

Since Wa was measured for the capacity determination, it 
is necessary only to measure the waste water to determine Ws- 
This may be done by allowing the waste to collect in a cahbrated 
tank. The head H may be found from the pressure gage read- 
ings, and Hs measured before the test. It is a good plan to use 
a float valve in the line which feeds the supply tank so that a 
constant level may be maintained in it automatically. 

(c) Curves of capacity, total amount of water supplied in 
gallons per twenty-four hours, and efficiency against the indepen- 
dent variable may be plotted from the data previously mentioned. 

Problem 69i. The capacity of a ram operating against 20 lbs. pressure 
is 1042 gals, per twenty-four hours, and its efficiency (Rankine) is 35 per 
cent. The supply level is 10.5 feet above the ram. How much water passes 
through the waste valve in gallons per twenty-four hours? 

Arts., 10,100 gals. 

Problem 69j. Using the data of the preceding problem, what is the 
D'Aubisson efficiency? Ans., 41%. 



70. Test of a Centrifugal Pump 

Principles. The useful work of a centrifugal pump is the 
product of a weight of water delivered in a given time in pounds 



70 MISCELLANEOUS TESTS 353 

and the total head pumped against in feet. The total head 
includes the friction heads of suction and discharge pipes and the 
velocity head. 

The work supplied to the pump is that received by its shaft 
in the case of a belt-driven machine, or one directly connected 
to an electric motor. In the case when the drive is a directly 
connected steam engine, both the drive and the pump are gen- 
erally tested as a single unit as would be a reciprocating pump. 

Selection of the Independent Variable. The rotative speed, 
quantity discharged, or head pumped against may be varied 
independently for a test. When one is varied arbitrarily, another 
is kept constant, and the third becomes a dependent variable. 
Two series of tests are useful; one at constant speed and the other 
at constant head, the independent variable being head and 
speed, respectively. When the speed is kept constant, the head 
may be varied by throttling the discharge, and when the head 
is kept constant, the speed is varied by control of the motor 
driving the pump. In the latter case, each change of speed 
must be accom^panied by a change in the valve opening in the 
discharge pipe in order to maintain a constant head. 

(a) Capacity may be expressed in gallons per twenty-four 
hours or per minute. The usual methods of measuring water 
rates mentioned under the heads of hydraulic turbines and 
reciprocating pumps, may be used. 

(b) Horse-power Supplied. The method of measuring this 
item depends upon the drive. If belt-driven, a transmission dyna- 
mometer is applicable. If motor driven, the motor should be 
calibrated (Test 74). If driven by a steam engine or turbine, it 
is generally more convenient to find the horse-power supplied to 
the set rather than to the pump alone. 

(c) The Water Horse-power may be calculated from the 
relation 

^•^•P- 33,000* 



354 



MISCELLANEOUS TESTS 



70 



W is the weight of the water discharged, in pounds per minute, 
measured as under (a). D is the total head pumped against, in 
feet, and may be determined as follows. Connect a pressure 
gage to the discharge pipe as close to the pump as possible. To 
the suction pipe, also close to the pump, connect a Bourdon gage or 
a mercury manometer. Call the indications of these instruments 

Pa = discharge gage reading, pounds per square inch; 
Psj P5 = suction gage reading, inches of mercury or pounds per 
square inch; 
/i = manometer reading, inches of mercuiy. 

Also let d and r/' represent the distances 
in feet between the gages as shown b}^ Fig. 
111. 

Assuming the diameters of the discharge 
and suction pipes equal, the velocity heads 
in these pipes will be equal. Then, since 
the energy WD added by the pump to the 
water equals the difference in energies on 
the discharge and suction sides (note that 
Ps is a negative pressure, counting from 
atmosphere), 

WD = Wx2,3Pa+d-WXi-lA3ps), 
and 

D = 2.3P,+d+l,13ps, . . . . (i) 




Fig. IIL — Measure- 
ment of Head. 



which relation is to be used when the 
suction pipe pressure is read with a vac- 
uum gage. Similarly, 

D = 2'3P,+d' + lA3h, .... (2) 

which is the appropriate relation when a mercurj^ manometer is 
employed. 



70 MISCELLANEOUS TESTS 355 

If the level of the water supplied is higher than the pump, a 
pressure gage is used in the suction pipe instead of a vacuum 
gage. Then the term 1.13^5 in equation (1) changes to — 2.3Ps, 
Ps being in pounds per square inch. Or, if a manometer is used, 
the term l.lSh in Eq. (2) changes to — 1.13/i. 

If the diameters of discharge and suction pipes are different, 
the change in velocity head should be credited to the pump. If 
Vd and Vs stand for the velocities in feet per second on the dis- 
charge and suction sides, respectively, then there should be 
added to D (as obtained from Eq. (1) or (2) ), the following: 



64.4 • 

The method of finding the head when testing a reciprocating 
pump (see p. 254), may also be used, but this does not credit the 
pump with the friction head in the suction pipe. 

(d) Hydraulic Efficiency may be calculated by dividing each 
value of water horse-power by the corresponding value of the 
horse-power supplied. 

(e) Curves may be plotted, from the data obtained, as follows : 
For constant speed tests, power supplied, capacity, and efficiency 
against head. For constant head tests, the same results plotted 
against speed. Sometimes speed or head, power supplied, and 
efficiency are plotted against quantity discharged. 

Problem 70i. How would you determine separately the work done by 
the various impellers of a stage centrifugal pump? 

Problem 7O2. Does or does not the measurement of total head by gages, 
outlined under (c), include the friction head of suction and discharge pipes, 
and why? Does it include the friction head of the water in passing through 
the pump, and ought this head to be included? Why? 

71. Test of a ^^ Power '^ Pump 

Principles. By '^ power '^ pump is meant a reciprocating 
pump driven by a crank shaft which receives its power through a 



356 MISCELLANEOUS TESTS 71 

belted pulley, or gears from a motor. The general principles to 
be studied for testing are similar to these previously outlined 
under Test 50. 

(a) Water Horse-power. See Tests 50 (a) and 70 (c). 

(b) Available Horse-power. This may be found as for a 
centrifugal pump, Test 70 (6), when the drive is by belt or geared 
motor. 

(c) Mechanical and Fluid Losses and Efficiencies. The dif- 
ference between the water horse-power and the indicated horse- 
power equals the hydraulic losses. The difference between the 
indicated horse-power and item (&) equals the mechanical losses. 
Expressions for the corresponding efficiencies are obvious. The 
total efficiency is item (a) divided by item (6). 

(d) Slip and Capacity. See Test 50 {d) and (e). 



72. Test of a Hoist 

Principles. A hoist is a machine by which a large weight 
may be lifted by the appUcation of a small force. This is 
accomplished usually by passing a chain, or chains, over a num- 
ber of w^heels geared together in such a way that a large motion 
of one end of the chain downward produces a small motion 
of the other end upward, whereby a mechanical advantage is 
obtained. 

The Ideal Mechanical Advantage is the ratio of a dis- 
tance moved through by the driving chain to the correspond- 
ing distance moved through by the following chain. Refer- 
ring to Fig. 112, representing a hoist diagrammatically, this 
ratio is D/d. If there were no friction, this would be the 
ratio of the weight lifted, Wy to the force applied F. As there 
is friction, 

The Actual Mechanical Advantage equals the ratio of the 
weight lifted to the force appUed, or W/F. 



i 



72 



MISCELLANEOUS TESTS 



357 




The efficiency of a hoist equals the work done in hfting 
the weight through any distance divided by the work done by 
the applied force acting through the corresponding 
distance. 

If the efficiency of a hoist is more than 50 per 
cent, the weight lifted will return by gravity when 
the hoisting force is removed unless there is a 
locking device. Where this is provided, it is ar- 
ranged to lock against the force of gravity only, and 
not against a force applied to the driving chain 
for the purpose of lowering the weight. 

(a) The Ideal Mechanical Advantage may be 
determined by actual measurement of the distances, 
D and d. Fig. 112. As d is generally very small 
compared with D, the result by this method may 

not have the desired degree of accuracy. A better method 
consists of counting the numbers of teeth of the various 
gears of the hoist and figuring from thedata obtained, by 
the principles of kinematics, the velocity ratio of driver to 
follower. 

(b) The Actual Mechanical Advantage may be determined 
by measuring the force applied to lift various loads. The desired 
results vary with the load, and may be plotted against its values. 
The loads may be applied by using various dead weights, suf- 
ficient to cover the working range of the hoist. The force required 
to lift these weights may be measured by applying the force 
through a spring balance hooked into the driving chain. Owing 
to the difficulty of reading a m.oving instrument, this is not 
a very accurate method. A better one is for the experimenter 
to stand on a platform scales and to apply the driving force 
at a uniform rate with one hand and at the same time, w^ith the 
other hand, to balance the scales by adjusting the jockey weight. 
The weight of the experimenter minus the reading of the scales 
then equals the force applied to the hoist. 



358 MISCELLANEOUS TESTS 72 

Several determinations of the force applied should be noted 
at each load, and their mean used to obtain the actual mechan- 
ical advantage at that load. It should not be attempted to make 
mental averages. 

(c) Efficiency equals (see Fig. 112) 

W 

Work done WXd F Actual mechanical advantage 



Work applied FXD D Ideal mechanical advantage ' 

"d 

Consequently each result under (b) may be divided by that 
under (a) to get the corresponding efficiency. The efficiencies 
should be plotted against the loads. 

Problem 72]. Assuming that the friction losses of a hoist are constant 
throughout its working range, deduce the form of, and sketch roughly, curves 
between force applied and load hfted and between efficiency and load lifted. 
Will these curves pass through the origin or not, and why? 

Problem 720. A differential hoist has 12 chain notches on the driving 
wheel and eleven on the smaller. What is its ideal mechanical advantage? 

Ans., 24. 

Problem 723. The efficiency of a hoist is 60 per cent and its ideal mechan- 
ical advantage is 40. What load will a force of 4 lbs. lift? Ans., 96 lbs. 

Problem 72 j. Prove that a hoist having an efficiency greater than 50 
per cent needs a locking device. 



73. Tests of Lubricating Oils 

Principles. The most indicative results of the relative 
values of lubricating oils are ol)tained from tests of viscosity, 
flash and chill points, and coefficient of friction. 

Viscosity manifests itself as internal friction of the oil, a prop- 
erty which opposes the motion of the particles upon themselves, 
resulting in a reluctance to flow. It is related to, but is not 
proportional to the density. Since it opposes motion, it is an 
undesirable property, but there is such a tiling as too little vis- 



73 MISCELLANEOUS TESTS 359 

cosity for good results. If the oil flows too readily, it may be 
squeezed out of the space between the surfaces it should lubricate, 
and the total amount of oil needed for proper lubrication 
might then become excessive. This depends largely upon the 
pressure between the bearing surfaces. 

The term ^^ body '' is also used to denote viscosity. 

The flash point is the temperature at which the oil will vaporize 
fast enough to form an explosive mixture with air. This tem- 
perature should be higher than the working temperature to be 
encountered in the service of the oil. Consequently it should be 
judged in connection with its service. 

The burning point is the temperature at which a body of the 
oil considered will burn w^hen a flame is placed a short distance 
over its surface. 

The chill point is the temperature at which the oil loses its 
fluidity. Its determination is necessary only when the tem- 
peratures during service are low. 

For more complete details concerning the requirements for 
and usual constants of lubricating oils, see Stillman's ^^ Engin- 
eering Chemistry'' or Marks' ^' Mechanical Engineer's Hand- 
book." 

(a) The Specific Gravity is of interest in connection with 
viscosity, since a high value of the one generally indicates a 
high value of the other. It may be determined by balancing 
a column of oil in one leg of a Li-tube against a column of water 
in the other leg. Then the specific gravity of the oil equals 
the height of the water column divided by the height of the oil 
column. A more convenient method is to use a hydrometer if 
one is available. 

Hydrometers are obtainable graduated to indicate specific 
gravity relative to the weight of water, but more usually they 
are graduated according to an arbitrary scale. The so-called 
Baume scale is largely used in the United States, although the 
more logical scale based on the weight of water is preferable. 



360 MISCELLANEOUS TESTS 73 

Hydrometers so graduated indicate Baume degrees (deg. Ee.). 
The relation between these degrees and specific gravity on the 
water basis is, for liquids heavier than water, 

Specific gravity = 145 -^ (145 — deg. Be.) 
and for liquids lighter than water, 

Specific gravity = 140-^ (130+deg. B6.) 

(b) Viscosity. This is a purely relative measurement. There 
are different standards for its expression, but, in general, it may 
be taken as the ratio of the time required by a given volume 
of the oil considered to flow through an orifice of a given size 
under a given head, or drop in head, to the time required by the 
same volume of another liquid, as water, to flow under the 
same conditions. 

The temperature of the oil has to do with its viscosity, so 
for comparative results the temperature must be kept constant 
during all tests. It should be remembered that the temperature 
during a test may be quite different from that in actual ser- 
vice, so the results are strictly comparative and not always 
indicative of the true merits of oils to be used at high tem- 
peratures. 

Apparatus for viscosity tests, or ^^ viscosimeters,'' may be 
readily improvised. It is desirable that the vessel containing 
the oil be water-jacketed to maintain a constant temperature. 
The orifice should be about xe in. in diameter. The head on 
the orifice may start at about 6 ins. and end at about 4 ins., 
the total volume of oil passing through the orifice being that 
between the levels at the start and finish. Some forms of 
viscosimeters are arranged so that the flow shall be under a con- 
stant head. 

(c) Flash, Burning, and Chill Points. The flash point may 
be foimd by placing the bulb of a mercury thermometer in a 



"^^ 



73 MISCELLANEOUS TESTS 361 

porcelain dish filled with oil to be tested, and heating the oil 
over a Bunsen burner until a flash may be obtained from it by 
passing a lighted taper over its surface. The temperature of 
the oil when this happens is noted as the flash point. The burn- 
ing point is found similarly, by carrying the heating to a point 
at which the flash causes a burning of the oil in the dish. The 
chill point may be found by chilling a small amount of the oil 
in the bottom of a test tube by surrounding it with a freezing 
mixture until it congeals. The test tube is then removed and 
the oil stirred with a thermometer until it has warmed sufficiently 
to flow^ from one end of the tube to the other. The temperature 
is then noted as the chill point. 

(d) Coeflicient of Friction. To determine this, an oil test- 
ing machine should be used. See Test 35. The oil to be tested 
should be used under the same bearing pressure and the same 
temperature as it will meet in service, as far as is possible. Com- 
parative tests of different oils should be made under uniform 
conditions of temperature, pressure and velocity, or else the 
results wall not be comparable. 

(e) Endurance Tests have to do with the total amount of 
oil necessary to secure required lubrication. An oil that is 
satisfactory in all other respects may be of prohibitive cost because 
its lack of body may necessitate a large rate of feed. An idea 
of the endurance of an oil may be formed by supplying the bear- 
ing of an oil tester with a limited amount of it and noting the 
time required to raise the temperature of the bearing a pre- 
determined amount. Another method is to note the time 
required to raise the coefficient of friction a predetermined amount. 
Still another is to measure the amount of oil during a given period 
of time when it is fed at a rate just sufficient to prevent a rise 
of temperature. 

Problem 73i. If the specific gravity of an oil is 0.85, what is its specific 
gravity in degrees Baume? If specific gravity is 1.15, what is its value in 
degrees Baume? Ans., 34.8°, 18.9°. 



362 MISCELLANEOUS TESTS 74 

74. Horse-power Test of an Electric Motor 

Principles. In mechanical engineering tests, it is often 
desirable to know the horse-power deUvered by an electric motor 
to the unit it drives, as, for example, a motor-driven centrifugal 
pump or blower. It then becomes necessar}^ to make a separate 
test of the motor. This can be done, of course, with a Prony 
brake by getting corresponding values of B.h.p. and current sup- 
plied. Such procedure is not always convenient, however, nor are 
the results as accurate as when the useful horse-power is found by 
the measurement of losses. Consequentl}^, the latter method will 
be described. The following notation will be used. 

V = voltage of Une ; 

A = armature current in amperes, motor loaded; 
Ao = armature current, motor running free; 
F = field current, amperes; 
/? = resistance of armature, ohms. 

Now the power delivered at an}- load, in watts, is 
746 X B.h.p. = watts input — losses. 

The losses ma}' be grouped as constant and variable. The 
variable loss to be considered is due to the armature resistance, 
increasing as the armature current increases, and equals A-R, 

The constant losses, entering the calculation, are due, first 
to friction and windage, and second, to hysteresis and eddy 
currents (the so-called '' iron losses '')• These losses may be 
considered constant at all loads, provided only that the speed is 
approximately constant. Now, when the motor is operated with- 
out load, the watts input equals the losses; and, since A^R losses 
at no load are very small, it follows: 

Constant losses = V{Ao+F). 



74 MISCELLANEOUS TESTS 363 

The watts input, under load, obviously equals 

V{A+F), 

Substituting these values of input and losses in the equation 
for B.h.p., we have 

746 B.h.p. = y(A+F)-A2i2-7(4o+F) 

= VA + VF-Am-VAQ-VF 

= A{V-AR)-VAq] 
and 

B.h.p. = .00134{4(F~Ai2)-7^o}. 

(a) Determination of Horse-power Output. In the equation 
last given, VAo and R are taken as constant, and may be prede- 
termined. Then, at any load applied to the motor, it is only 
necessary to measure the armature current, A, corresponding 
to that load, and the voltage; F, in order to calculate the B.h.p. 

The armature resistance, R, may be determined by the 
''drop of potential'' method. The armature being stationary, 
connect the armature leads to the line with a resistance and 
ammeter in series, being careful to avoid injury to the coils with 
excessive current. Measure the amperes flowing, and the E.m.f. 
drop across the brushes with a voltmeter. Then 

Resistance, ohms = 72 = — t -. 

Amperes 

This should be repeated for a number of different positions of the 
armature, and the average resistance from the various positions 
taken. Repeat, also, for another value of the current. 

Next, the motor should be connected as in service, but with 
an ammeter in the armature circuit, and a voltmeter to indicate 
the voltage at the armature terminals. It is then run at no load 
for a period of fifteen to thirty minutes, in order to obtain uniform 



^^^ 



364 MISCELLIXEOUS TESTS 74 

conditions of friction, etc. If, now, the armature current is read, 
this furnishes the required value of VAq. 

If the motor is equipped with a rheostatic control, giving 
it different speeds, the no load value of the armature watts. 
AT^o, should be determined at each different speed at which the 
motor is to be run, and a speed-ampere curve drawn. Then, 
when the motor is operating under load, it is necessar}^ not onl}- 
to read the armature amperes, but also the speed in order to 
appl}^ the corresponding value of AVo in the B.h.p. formula. 

(b) Efficiency. If this is required, it is only necessarj^ to 
obtain the total watts input. This divided into the watts out- 
put equals the efficiency. For a shunt wound constant speed 
motor, the field current, being approximately constant, ma}' be 
predetermined and added as a constant to the armature current 
to get the total amperes input. 

Problem 74i. At no load, a motor takes 10.5 amperes armature current 
at 220 volt?. What is the value of AT'o? Is this what is referred to as the 
"constant " loss? What is the constant loss, in watts (see Problem 743)? 

Afis., 2310 watts. 
Problem 74:. Same motor, given the armature resistance = 0.038 ohm. 
What is the brake horse-power, when the armature current is 150 amperes? 

Arts., 40 B.h.p. 
Problem 74^. What is the efficiency of the preceding, if the field current 
is 5.8 amperes. Ans., 87 per cent. 



APPENDIX 



LOGARITHMS 
To Find the Fractional Power of a Number Less than Unity. 

To avoid the use of negative characteristics, the following 
rule is suggested. 

Rule. Express the given number as a fraction whose numer- 
ator is unity. Find the required power of the denominator of 
this fraction, and then reduce to a decimal. 

For example, 

To find 0.787l•^^ 

Log. 1.27'-''=' = 1.33X0.1C4 = 0.138; 
0.138 = log 1.37; 
.'. 1.271-33 = 1.37, 

1 1 



and .7871-33 



1.271-33 1.37 
= 0.73. 



To Find the Napierian Logarithm (Base e =2.718) of a Number. 

Rule. Multiply the common logarithm (base 10) by the 
constant 2.302, or 2.3, approximately. 
For example. 

To find log. of 315, (see page 366). 
Logio 315 = 2.498, 
.-. Log. 315 = 2.3X2.498 = 5.750. 

S65 



366 



APPENDIX 



COMMON LOGARITHMS 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Dif. 

42 








0000 


3010 


4771 


6021 


6990 


7782 


8451 


9031 


9542 


10 


0000 


0043 


0086 


0128 


0170 


{J'Z12 


0253 


0294 


0334 


0374 


11 


0414 


0453 


0492 


0531 


0569 


0607 


0645 


0682 


0719 


0755 


38 


12 


0792 


0828 


0864 


0899 


0934 


0969 


1004 


1038 


1072 


1106 


35 


13 


1139 


1173 


1206 


1239 


1271 


1303 


1335 


1367 


1399 


1430 


32 


14 
15 


1461 


1492 


1523 


1553 


1584 


1614 
1903 


1644 
1931 


1673 
1959 


1703 
1US7 


1732 
2014 


30 

28 


1761 


1790 


1818 


1847 


1875 


16 


2041 


2068 


2095 


2122 


2148 


2175 


2201 


2227 


2253 


2279 


26 


17 


2304 


2330 


2355 


2380 


2405 


2430 


2455 


2480 


2504 


2529 


25 


18 


2553 


2577 


2601 


2625 


2648 


2672 


2695 


2718 


2742 


2765 


24 


19 
20 


2788 


2810 


2833 


2856 


2878 


2900 


2923 


2945 


2967 


2989 


22 
21 


3010 


3032 


3054 


3075 


3096 


3118 


3139 


3160 


3181 


3201 


21 


3222 


3243 


3263 


3284 


3304 


3324 


3345 


3365 


3385 


3404 


20 


22 


3424 


3444 


3464 


3483 


3502 


3522 


3541 


3560 


3579 


3598 


19 


23 


3617 


3636 


3655 


3674 


3692 


3711 


3729 


3747 


3766 


3784 


19 


24 
26 


3802 


3820 


3838 


3856 


3874 


3892 
4065 


3909 
4082 


3927 
4099 


3945 
4116 


3962 
4133 


18 
17 


3979 


3997 


4014 


4031 


4048 


26 


4150 


4166 


4183 


4200 


4216 


4232 


4249 


4265 


4281 


4298 


16 


27 


4314 


4330 


4346 


4362 


4378 


4393 


4409 


4425 


4440 


4456 


16 


28 


4472 


4487 


4502 


4518 


4533 


4548 


4564 


4579 


4594 


4609 


15 


29 


4624 


4639 


4654 


4669 


4683 


4698 


4713 


4728 


4742 


4757 


15 
14 


30 


4771 


4786 


4800 


4814 


4829 


4843 


4857 


4871 


4886 


4900 


31 


4914 


4928 


4942 


4955 


4969 


4983 


4997 


5011 


5024 


5038 


14 


32 


5051 


5065 


5079 


5092 


5105 


5119 


5132 


5145 


5159 


5172 


13 


33 


5185 


5198 


5211 


5224 


5237 


5250 


5263 


5276 


5289 


5302 


13 


34 
35 


5315 


5328 


5340 


5353 


5366 


5378 


5391 


5403 


5416 


5428 


13 


5441 


5453 


5465 


5478 


5490 


5502 


5514 


5527 


5539 


5551 


12 


36 


5563 


5575 


5587 


5599 


5611 


5623 


5635 


5647 


5658 


5670 


12 


37 


5682 


5694 


5705 


5717 


5729 


5740 


5752 


5763 


5775 


5786 


12 


38 


5798 


5809 


5821 


5832 


5843 


5855 


5866 


5877 


5888 


5899 


11 


39 
40 


5911 


5922 


5933 


5944 


5955 


5966 


5977 


5988 


5999 


6010 


11 
11 


6021 


6031 


6042 


6C53 


6064 


6075 


6085 


6096 


6107 


6117 


41 


6128 


6138 


6149 


6160 


6170 


6180 


6191 


6201 


6212 


6222 


10 


42 


6232 


6243 


6253 


6263 


6274 


6284 


6294 


6304 


6314 


6325 


10 


43 


6335 


6345 


6355 


6365 


6375 


6385 


6395 


6405 


6415 


6425 


10 


44 


6435 


6444 


6454 


6464 


6474 


6484 


6493 


6503 


6513 


6522 


10 
10 


45 


6532 


6542 


6551 


6561 


6571 


6580 


6590 


6599 


6609 


6618 


46 


6628 


6637 


6646 


6656 


6665 


6675 


6684 


6693 


6702 


6712 


9 


47 


6721 


6730 


6739 


6749 


6758 


6767 


6776 


6785 


6794 


6803 


9 


48 


6812 


6821 


6830 


6839 


6848 


6857 


6866 


6875 


6884 


6893 


9 


49 
50 


6902 


6911 


6920 
7007 


6928 
7016 


6937 
7024 


6946 


6955 


6964 


6972 


6981 


9 
9 


6990 


6998 


7033 


7042 


7050 


7059 


7067 


51 


7076 


7084 


7093 


7101 


7110 


7118 


7126 


7135 


7143 


7152 


9 


52 


7160 


7168 


7177 


7185 


7193 


7202 


7210 


7218 


7226 


7235 


8 


53 


7243 


7251 


7259 


7267 


7275 


7284 


7292 


7300 


7308 


7316 


8 


54 


7324 


7332 


7340 


7348 


7356 


7364 


7372 


7380 


7388 


7396 


8 



APPENDIX 



367 



COMMON LOGARITHMS 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Dif. 
8 


55 


7404 


7412 


7419 


7427 


7435 


7443 


7451 


7459 


7466 


7474 


56 


7482 


7490 


7497 


7505 


7513 


7520 


7528 


7536 


7543 


7551 


8 


57 


7559 


7566 


7574 


7582 


7589 


7597 


7604 


7612 


7619 


7627 


8 


58 


7634 


7642 


7649 


7657 


7664 


7672 


7679 


7686 


7694 


7701 


7 


59 
SO 


7709 


7716 


7723 


7731 


7738 


7745 


7752 


7760 


7767 


7774 


7 
7 


7782 


7789 


7796 


7803 


7810 


7818 


7825 


7832 


7839 


7846 


61 


7853 


7860 


7868 


7875 


7882 


7889 


7896 


7903 


7910 


7917 


7 


62 


7924 


7931 


7938 


7945 


7952 


7959 


7966 


7973 


7980 


7987 


7 


63 


7993 


8000 


8007 


8014 


8021 


8028 


8035 


8041 


8048 


8055 


7 


64 
65 


8062 


8069 


8075 


8082 


8089 


8096 


8102 


8109 


8116 


8122 


7 
7 


8129 


8135 


8142 


8149 


8156 


8162 


8169 


8176 


8182 


8189 


66 


8195 


8202 


8209 


8215 


8222 


8228 


8235 


8241 


8248 


8254 


7 


67 


8261 


8267 


8274 


8280 


8287 


8293 


8299 


8306 


8312 


8319 


6 


68 


8325 


8331 


8338 


8344 


8351 


8357 


8363 


8370 


8376 


8382 


6 


69 
70 


8388 


8395 


8401 


8407 


8414 


8420 


8426 


8432 


8439 


8445 


6 


8451 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 


8506 


6 


71 


8513 


8519 


8525 


8531 


8537 


8543 


8549 


8555 


8561 


8567 


6 


72 


8573 


8579 


8585 


8591 


8597 


8603 


8609 


8615 


8621 


8627 


6 


73 


8633 


8639 


8645 


8651 


8657 


8663 


8669 


8675 


8681 


8686 


6 


74 
75 


8692 


8698 


8704 


8710 


8716 


8722 


8727 


8733 


8739 


8745 


6 


8751 


8756 


8762 


8768 


8774 


8779 


8785 


8791 


8797 


8802 


6 


76 


8808 


8814 


8820 


8825 


8831 


8837 


8842 


8848 


8854 


8859 


6 


77 


8865 


8871 


8876 


8882 


8887 


8893 


8899 


8904 


8910 


8915 


6 


78 


8921 


8927 


8932 


8938 


8943 


8949 


8954 


8960 


8965 


8971 


6 


79 
80 


8976 


8982 


8987 


8993 


8998 


9004 


9009 


9015 


9020 


9025 


5 
5 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 


81 


9085 


9090 


9096 


9101 


9106 


9112 


9117 


9122 


9128 


9133 


5 


82 


9138 


9143 


9149 


9154 


9159 


9165 


9170 


9175 


9180 


9186 


5 


83 


9191 


9196 


9201 


9206 


9212 


9217 


9222 


9227 


9232 


9238 


5 


84 


9243 


9248 


9253 


9258 


9263 


9269 


9274 


9279 


9284 


9289 


5 


85 


9294 


9299 


9304 


9309 


9315 


9320 


9325 


9330 


9335 


9340 


5 


86 


9345 


9350 


9355 


9360 


9365 


9370 


9375 


9380 


9385 


9390 


5 


87 


9395 


9400 


9405 


9410 


9415 


9420 


9425 


9430 


9435 


9440 


5 


88 


9445 


9450 


9455 


9460 


9465 


9469 


9474 


9479 


9484 


9489 


5 


89 
90 


9494 


9499 


9504 


9509 


9513 


9518 


9523 


9528 


9533 


9538 


5 
5 


9542 


9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 


91 


9590 


9595 


9600 


9605 


9609 


9614 


9619 


9624 


9628 


9633 


5 


92 


9638 


9643 


9647 


9652 


9657 


9661 


9666 


9671 


9675 


9680 


5 


93 


9685 


9689 


9694 


9699 


9703 


9708 


9713 


9717 


9722 


9727 


5 


94 


9731 


9736 


9741 


9745 


9750 


9754 


9759 


9763 


9768 


9773 


5 
5 


95 


9777 


9782 


9786 


9791 


9795 


9800 


9805 


9809 


9814 


9818 


96 


9823 


9827 


9832 


9836 


9841 


9845 


9850 


9854 


9859 


9863 


4 


97 


9868 


9872 


9877 


9881 


9886 


9890 


9894 


9899 


9903 


9908 


4 


98 


9912 


9917 


9921 


9926 


9930 


9934 


9939 


9943 


9948 


9952 


4 


99 


9956 


9961 


9965 


9969 


9974 


9978 


9983 


9987 


9991 


9996 


4 



368 



APPENDIX 





DIAMETERS AND AREAS 


OF CIRCLES 






Diam. 


Area. 


Diam. 


Area. 


Diam. 


Area. 


Diam. 


Area. 


Diam. 


Area. 


A 


.00307 


H 


6.78 


~H~ 


26.5 


t 


102. 


i 


230. 


i 


.0123 


3. 


7.07 


7 
8 


27.1 




104. 


1 

4 


234. 


A 


.0276 


A 


7.37 


11 


27.7 


1 


106. 


3 

8 


237. 


1 
4 


.0491 


i 


7.67 


6. 


28.3 


3 
4 


108. 


i 


240. 


A 


.0767 


A 


7.98 


i 

8 


29.5 


7 
8 


111. 


f 


244. 


1 


.110 


1- 
■1 


8.30 


1 
it 


30.7 


12. 


113. 


f 


247. 


A 


.150 


A 


8.62 




31.9 


i 


115. 


7 
8 


251. 


i 


.196 


3 

8 


8.95 


1 


33.2 


i 


118. 


18. 


254. 


A 


.248 


A 


9.28 


1 


34.5 


i 


120. 


i 


258. 


1 


.307 


1 

2 


9.62 


3 
4 


35.8 


1 

2 


123. 


-1- 


262. 


H 


.371 


A 


9.97 


7 
8 


37.1 


5 

8 


125. 


1 


265. 


3 
4 


.442 


5 

8 


10.3 


7. 


38.5 


i 


128. 


i 


269. 


H 


.518 


H 


10.7 


i 


39.9 


7 
8 


130. 


5 

8 


272. 


7 
8 


.601 


3 
4 


11.0 


1 

4 


41.3 


13. 


133. 


f 


276. 


U 


.690 


13. 
16 


11.4 


f 


42.7 


1 


135. 


1 


280. 


1. 


.785 


i 


11.8 


1 
2 


44.2 


1 

4 


138. 


19. 


283. 


A 


.887 


H 


12.2 


5 

8 


45.7 


1 


140. 


1 

8 


287. 


1 


.994 


4. 


12.6 


3 
4 


47.2 


1 


143. 


i 


291. 


A 


1.11 


A 


13.0 


i 


48.7 


1 


146. 


3 

8 


295. 


, i 


1.23 


i 


13.4 


8. 


50.3 


1 

4 


148. 


1 


299. 


A 


1.35 


16 


13.8 


1 
8 


51.8 


1 


151. 


1 


302. 


f 


1.48 


i 


14.2 


4 


53.5 


14. 


154. 


3 
4 


306. 


A 


1.62 


A 


14.6 


3 

8 


55.1 


1 

8 


157. 


7 
8 


310. 


j 


1.77 


3 

"8 


15.0 


1 


56.7 


1 


159. 


20. 


314. 




1.92 


A 


15.5 




58.4 




162. 


1 

8 


318. 


1 


2.07 


i 

2 


15.9 


3 
4 


60.1 


1 
2 


165. 


i 


322. 


16 


2.24 


9 

16 


16.3 


7 
"8 


61.9 


t 


168. 


f 


326. 


3 

4 


2.40 


5 

8 


16.8 


9. 


63.6 


3 

4 


171. 


§ 


330. 


H 


2.58 


H 


17.3 


1 

8 


65.4 


7 
8 


174. 


5 

8 


334. 


1 


2.76 


3 
4 


17.7 


1 


67.2 


15. 


177. 


1 


338. 


H 


2.95 


a 


18.2 




69.0 


i 


180. 


i 


342. 


2. 


3.14 


i 


18.7 


1 
2 


70.9 


i 
4 


183. 


21. 


346. 


A 


3.34 


a 


19.1 


5 
8 


72.8 


f 


186. 


1 


350. 


i 


3.55 


5. 


19.6 


1 


74.7 


f 


189. 


i 

4 


355. 


A 


3.76 


16 


20.1 


J 


76.6 




192. 




359. 


i 


3.98 


1 


20.6 


10. 


78.5 


3 

4 


195. 


1 


363. 


A 


4.20 


A 


21.1 


1 


80.5 


7 
8 


198. 


f 


367. 


f 


4.43 


1 

4 


21.6 


i 


82.5 


16. 


201. 


i 


371. 


A 


4.67 


A 


22.2 


3 

8 


84.5 


i 


204. 


7 
8 


376. 


h 


4.91 


3 

8 


22.7 


1 
2 


86.6 


1 

4 


207. 


22. 


380. 


A 


5.16 


A 


23.2 


1 


88.7 


.3 

8 


211. 


i 


384. 


5 

8 


5.41 


1 

2 


23.8 


I 


90.8 


1 

2 


214. 


1 

4 


389. 


H 


5.67 


9 
16 


24.3 


7 
8 


92.9 


1 


217. 


1 


393. 


1 


5.94 


5 

"8 


24.8 


11. 


95.0 


3 
4 


220. 


1 

2 


398. 


H 


6.21 


\i 


25.4 


1 
8 


97.2 


7 
"8 


224. 


5 

8 


402. 


7 
8 


6.49 


3 
4 


26.0 


i 


99.4 


17. 


227. 


1 


406. 



APPENDIX 
DIAMETERS AND AREAS OF CIRCLES— Conhnwed 



369 



Diam. 


Area. 


Diam. 


Area. 


Diam. 


Area 


Diam. 


Area. 


Diam. 


Area. 


1 


411. 


1 


466. 


7 
8 


525. 


i 


588. 


7 
8 


654. 


23. 


415. 


i 


471. 


26. 


531. 


i 


594. 


29. 


660. 


J 


420. 


5 

8 


476. 


i 


536. 


i 


599. 


1 

8 


666. 


1 

4 


425. 


3 
4 


481. 


1 

4 


541. 


3 
4 


605. 


i 


672. 


^ 


429. 


8 


485. 


3 

8 


546. 


i 


610. 


1 


677. 


* 


434. 


25. 


491. 


i 


551. 


28. 


616. 


1 
2 


683. 


i 


438. 


1 

8 


495. 


f 


556. 


J 


621. 


5 

8 


689. 


3 
4 


443. 


1 
4 


501. 


3 
4 


562. 


1 

4 


627. 


f 


695. 


7 
8 


448. 


3 

8 


505. 


7 
8 


567. 


3 

8 


632. 


i 


700. 


24. 


452. 


1 
2 


511. 


27. 


573. 


1 
2 


638. 


30. 


707. 


i 


457. 


5 

8 


515. 


1 

8 


577. 


5 

8 


643. 






i 


462. 


i 


521. 


i 


583 


f 


649. 







WEIGHT OF ONE CUBIC FOOT OF WATER AT VARIOUS 

TEMPERATURES 



Temp., Deg. F. 


1 

Weight, Lbs. per 
Cu. Ft. 


Temp., Deg. F. 


Weight, Lbs. per 
Cu. Ft. 


30 


62.42 


190 


60.36 


40 


62.43 


200 


60.12 


50 


62.42 


210 


59.88 


60 


62.37 


220 


59.63 


70 


62.30 


230 


59.37 


80 


62.22 


240 


59.11 


90 


62.11 


250 


58.83 


100 


62.00 


260 


58.55 


110 


61.86 


270 


58.26 


120 


61.71 


280 


57.96 


130 


61.55 


290 


57.65 


140 


61.38 


300 


57.33 


150 


61.20 


310 


57.00 


160 


61.00 


320 


. 56.66 


170 


60.80 


330 


56.30 


180 


60.58 


340 


55.94 



370 



APPENDIX 



STEAM TABLES FOR CONDENSER CALCULATIONS 

Revised from Marks' Mechanical Engineers' Handbook. 





Vacuum in In. 










Temperature 
Deg. Fahr. 


of Mercury 
Referred to a 

30-in. Bar. 
(Mercury at 

58.4° F.) 


Pressure Lb. 

Per Sq. In. 

Absolute 


Specific Vol- 
ume Cu. Ft. 
Per Lb. 


Heat of the 
Liquid 


Total Heat of 
the Steam 


50 


29.637 


0.1780 


1702.0 


18.08 


1081.4 


52 


29.609 


0.1917 


1586.0 


20.08 


1082.3 


54 


29.579 


0.2063 


1480.0 


22.08 


1083.2 


56 


29.547 


0.2219 


1381.0 


24.08 


1084.1 


58 


29.513 


0.2385 


1291.0 


26.08 


1085.0 


60 


29.477 


0.2562 


1208.0 


28.08 


1085.9 


62 


29.439 


0.2749 


1130.0 


30.08 


1086.8 


64 


29.398 


0.2949 


1058.0 


32.07 


1087.6 


66 


29.354 


0.3161 


991.0 


34.07 


1088.5 


68 


29.308 


0.3386 


928.0 


36.07 


1089.4 


70 


29.259 


0.3626 


871.0 


38.06 


1090.3 


72 


29.208 


p. 3880 


817.0 


40.05 


1091.2 


74 


29.153 


0.4148 


767.0 


42.05 


1092.1 


76 


29.095 


0.4432 


720.0 


44.04 


1093.0 


78 


29.034 


0.4735 


677.0 


46.04 


1093.9 


80 


28.968 


0.505 


636.8 


48.03 


1094.8 


82 


28.899 


0.539 


598.7 


50.03 


1095.6 


84 


28.826 


0.575 


562.9 


52.02 


1096.5 


86 


28.749 


0.613 


529.5 


54.01 


1097.4 


88 


28.666 


0.654 


498.4 


56.01 


1098.3 


90 


28.580 


0.696 


469.3 


58.00 


1099.2 


92 


28.489 


0.741 


442.2 


60.00 


1100.1 


94 


28.392 


0.789 


417.0 


61.99 


1101.0 


96 


28.290 


0.838 


393.4 


63.98 


1101.8 


98 


28.183 


0.891 


371.4 


65.98 


1102.8 


100 


28.070 


0.946 


350.8 


67.97 


1103.6 


102 


27.951 


1.005 


331.5 


69.96 


1104.5 


104 


27 . 825 


1.066 


313.3 


71.96 


1105.3 


106 


27.692 


1.131 


296.4 


73.95 


1106.2 


108 


27.550 


1.199 


280.5 


75.95 


1107.1 


110 


27.404 


1.271 


265.5 


77.94 


1108.0 


112 


27.250 


1.346 


251.4 


79.93 


1108.8 


114 


27.088 


1.426 


238.2 


81.93 


1109.7 


1 116 


26.919 


1.509 


225.8 


83.92 


1110.6 


118 


26.739 


1.597 


214.1 


85.92 


1111.5 


120 


26.553 


1.689 


203. 1 


87.91 


1112.3 


122 


26.355 


1.785 


192.8 


89.91 


1113 2 


124 


26.149 


1.886 


183.1 


91.90 


1114.1 


126 


25.931 


1.992 


173.9 


93.90 


1115.0 


128 


25.706 


2.103 


165.3 


95.89 


1115.8 


130 


25.48 


2.219 


157.1 


97.89 


1116.7 


135 


24.84 


2.53 


138.7 


102.9 


1118.8 


140 


24.12 


2.88 


122.8 


107.9 


1121.0 


145 


23.33 


3.28 


109.0 


112.9 


1123.1 


150 


1 22.43 


3.71 


96.9 


117.9 


1125.3 



APPENDIX 



371 



PROPERTIES OF SATURATED STEAM 

REPRODUCED FROM MARKS AND DAVIs' ^' STEAM TABLES AND DIAGRAMS 
(Copyright, 1909, by Longmans, Green & Co.) 



Pressure, 

Pounds 

Absolute. 


Tempera- 
ture Deg. 
F. 


Density 
Lbs. per 
Cu. Ft. 


Specific 

Volume Cu. 

Ft. per 

Pound 

333.0 


Heat of the 
Liquid 
B.t.u. 

h 


Latent Heat 

of Evap. 

B.t.u. 

L 


Total Heat 

of Steam 

B.t.u. 

H 


1 


101.83 


.00300 


69.8 


1034.6 


1104.4 


2 


126.15 


.00576 


173.5 


94.0 


1021.0 


1115.0 


3 


141.52 


.00845 


118.5 


109.4 


1012.3 


1121.6 


4 


153.01 


.0111 


90.5 


120.9 


1005.7 


1126.5 


5 


162.28 


.0136 


73.33 


130.1 


1000.3 


1130.5 


6 


170.06 


.0162 


61.89 


137.9 


995.8 


1133.7 


7 


176.85 


.0187 


53.56 


144.7 


991.8 


1136.5 


8 


182.86 


.0211 


47.27 


150.8 


988.2 


1139.0 


9 


188.27 


.0236 


42.36 


156.2 


985.0 


1141.1 


10 


193.22 


.0261 


38.38 


161.1 


982.0 


1143.1 


11 


197.75 


.0285 


35.10 


165.7 


979.2 


1144.9 


12 


201.96 


.0309 


32.36 


169.9 


976.6 


1146.5 


13 


205.87 


.0333 


30.03 


173.8 


974.2 


1148.0 


14 


209.55 


.0357 


28.02 


177.5 


971.9 


1149.4 


14.7 


212 


.0375 


26.73 


180 


970.4 


1150.4 


15 


213.0 


.0381 


26.27 


181.0 


969.7 


1150.7 


16 


216.3 


.0404 


24.79 


184.4 


967.6 


1152.0 


17 


219.4 


.0428 


23.38 


187.5 


965.6 


1153.1 


18 


222.4 


.0451 


22.16 


190.5 


963.7 


1154.2 


19 


225.2 


.0475 


21.07 


193.4 


961.8 


1155.2 


20 


228.0 


.0498 


20.08 


196.1 


960.0 


1156.2 


22 


233.1 


.0545 


18.37 


201.3 


956.7 


1158.0 


24 


237.8 


.0591 


16.93 


206.1 


953.5 


1159.6 


26 


242.2 


.0636 


15.72 


210.6 


950.6 


1161.2 


28 


246.4 


.0682 


14.67 


214.8 


947.8 


1162.6 


30 


250.3 


.0728 


13.74 


218.8 


945.1 


1163.9 


32 


254.1 


.0773 


12.93 


222.6 


942.5 


1165.1 


34 


257.6 


.0818 


12.22 


226.2 


940.1 


1166.3 


36 


261.0 


.0863 


11.58 


229.6 


937.7 


1167.3 


38 


264.2 


.0908 


11.01 


232.9 


935.5 


1168.4 


40 


267.3 


.0953 


10.49 


236.1 


933.3 


1169.4 


42 


270.2 


.0998 


10.02 


239.1 


931.2 


1170.3 


44 


273.1 


.104 


9.59 


242.0 


929.2 


1171.2 


46 


275.8 


.109 


9.20 


244.8 


927.2 


1172.0 


48 


278.5 


.113 


8.84 


247.5 


925.3 


1172.8 



372 




APPENDIX 








PROPERTIES 


OF SATURATED STEAM 




Pressure, 

Pounds 

Absolute. 


Tempera- 
ture Deg. 
F. 


Density 
Lbs. per 
Cu. Ft. 


Specific * 
Volume Cu. 
Ft. Per 
Pound. 


Heat of the 

Liquid 

B.t.u. 

h 


1 

Latent Heat 

of Evap. 

B.t.u. 

L 


Total Heat 

of Steam 

B.t.u. 

H 


50 


281.0 


.117 


8.51 


250.1 


923.5 


1173.6 


52 


283.5 


.122 


8.20 


252.6 


921.7 


1174.3 


64 


285.9 


.126 


7.91 


255.1 


919.9 


1175.0 


66 


288.2 


.131 


7.65 


257.5 


918.2 


1175.7 


68 


290.5 


.135 


7.40 


259.8 


916.5 


1176.4 


60 


292.7 


.139 


7.17 


262.1 


914.9 


1177.0 


62 


294.9 


.144 


6.95 


264.3 


913.3 


1177.6 


64 


297.0 


.148 


6.75 


266.4 


911.8 


1178.2 


66 


299.0 


.152 


6.56 


268.5 


910.2 


1178.8 


68 


301.0 


.157 


6.38 


270.6 


908.7 


1179.3 


70 


302.9 


.161 


6.20 


272.6 


907.2 


1179.8 


72 


304.8 


.166 


6.04 


274.5 


905.8 


1180.4 


74 


306.7 


.170 


5.89 


276.5 


904.4 


1180.9 


76 


308.5 


.174 


5.74 


278.3 


903.0 


1181.4 


78 


310.3 


.179 


5.60 


280.2 


901.7 


1181.8 


80 


312.0 


.183 


5.47 


282.0 


900.3 


1182.3 


82 


313.8 


.187 


5.34 


283.8 


899.0 


1182.8 


84 


315.4 


.191 


5.22 


285.5 


897.7 


1183.2 


86 


317.1 


.196 


5.10 


287.2 


896.4 


1183.6 


88 


318.7 


.200 


5.00 


288.9 


895.2 


1184.0 


90 


320.3 


.204 


4.89 


290.5 


893.9 


1184.4 


92 


321.8 


.209 


4.79 


292.1 


892.7 


1184.8 


94 


323.4 


.213 


4.69 


293.7 


891.5 


1185.2 


96 


324.9 


.217 


4.60 


295.3 


890.3 


1185.6 


98 


326.4 


.221 


4.51 


296.8 


889.2 


1186.0 


100 


327.8 


.226 


4.429 


298.3 


888.0 


1186.3 


105 


331.4 


.236 


4.230 


302.0 


885.2 


1187.2 


110 


I 334.8 


.247 


4.047 


305.5 


882.5 


1188.0 


115 


338.1 


.258 


3.880 


309.0 


879.8 


1188.8 


120 


341.3 


.268 


3.726 


312.3 


877.2 


1189.6 


125 


344.4 


.279 


3.583 


315.5 


874.7 


1190.3 


130 


347.4 


.290 


3.452 


318.6 


872.3 


1191.0 


135 


350.3 


.300 


3.331 


321.7 


869.9 


1191.6 


140 


353 . 1 


.311 


3.219 


324.6 


867.6 


1192.2 


145 


355.8 


.321 


3.112 


327.4 


865.4 


1192.8 



APPENDIX 



373 



PROPERTIES OF SATURATED STEAM 



Pressure 

Pounds 

Absolute. 


! 

Tempera- 
ture Deg. 
F. 


Density 
Lbs. per 
Cu. Ft. 


Specific 

Volume Cu. 

Ft. per 

Pound. 


Heat of the 
Liquid, 
B.t.u. 

h 


Latent Heat 

of Evap., 

B.t.u. 

L 


Total Heat 

of Steam, 

B.t.u. 

H 


150 


358.5 


.332 


3.012 


330.2 


863.2 


1193.4 


155 


361.0 


.342 


2.920 


332.9 


861.0 


1194.0 


160 


363.6 


.353 


2.834. 


335.6 


858.8 


1194.5 


165 


366.0 


.363 


2.753 


338.2 


856.8 


1195.0 


170 


368.5 


.374 


2.675 


340.7 


854.7 


1195.4 


175 


370.8 


.384 


2.602 


343.2 


852.7 


1195.9 


180 


373.1 


.395 


2.553 


345.6 


850.8 


1196.4 


185 


375.4 


.405 


2.468 


348.0 


848.8 


1196.8 


190 


377.6 


.416 


2.406 


350.4 


846.9 


1197.3 


195 


379.8 


.426 


2.346 


352.7 


845.0 


1197.7 


200 


381.9 


.437 


2.290 


354.9 


843.2 


1198.1 


205 


384.0 


.447 


2.237 


357.1 


841.4 


1198.5 


210 


386.0 


.457 


2.187 


359.2 


839.6 


1198.8 


215 


388.0 


.468 


2.138 


361.4 


837.9 


1199.2 


220 


389.9 


.478 


2.091 


363.4 


836.2 


1199.6 


225 


391.9 


.489 


2.046 


365.5 


834.4 


1199.9 


230 


393.8 


.499 


2.004 


367.5 


832.8 


1200.2 


235 


395.6 


.509 


1.964 


369.4 


831.1 


1200.6 


240 


397.4 


.520 


1.924 


371.4 


829.5 


1200.9 


245 


399.3 


.530 


1.887 


373.3 


827.9 


1201.2 


250 


401.1 


.541 


1.850 


375.2 


826.3 


1201.5 



374 



APPENDIX 



Temperciturs and l^eaf of Liquid 

180 200 220 240 260 280 500 320 MO 360 380 
Ldtenf Heat 

640 660 880 900 920 940 960 980 







025 0X)75 0.125 0.175 0225 Q275 0.325 0.375 0.425 0.475 li60 1130 

n s i t y >-i<-Jofo\ HeatH 



1200 



D 



Temperature and Heofof Liquid 
70 90 110 130 150 170 IPO 2|0 



960 



Lcitent Heat 
9S0 1000 1020 




1040 



0.0025 0.007S 0.0125 Q0I75 0.0225 00275 00325 iiOO 



PowEt^ [-<-•• 



--D e n 5 I t 



1120 1140 
Total Heat-J 



1130 



Fig. 113. — Properties of Steam. 



"''^^ 



APPENDIX 375 



CURVES OF THE PROPERTIES OF SATURATED STEAM 

(Reprinted from Power ^ Nov. 17, 1914) 

Explanation 

Heat quantities may be read to the nearest unit; that is, to 
within about one B.t.u. or degree F. for any pressure between 
1 and 230 lbs. absolute. The upper part of the chart deals with 
pressures above atmosphere, and the lower part, pressures below 
atmosphere. 

To use the chart, find the given pressure on the left-hand 
scale, and follow the horizontal line at this pressure until it inter- 
sects the curve of the property sought; then follow vertically to 
the corresponding scale. 

If temperature is given instead of pressure, use the tempera- 
ture curve in place of the pressure scale. 



376 



APPENDIX 



1350 



1300 



1250 



1200 



1150 



1 100 



1050 



1000 



950 



900 



850 



800 



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146 150 IM 158 1j62 1.66 1.70 

MOLLIER DIAGRAM < STEAM > 



174 Dd 



■"I!" 



APPENDIX 



g 


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^ 


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g 


^••SZ' 


s^ 


S 


^ 


1 


^ 


^ 


7^ 




g 


^ 


^ 






^ 


3 






S 


^ 


~r'--~- 


:^ 




^2^ 


7^ 






2^ 


sa 


^ 


1 




^ 


?^ 


^^ 


:2f 




^ 






^ 




^^^ 


i 


!^ 






^ 


^ 




^ 


^ 


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^ 




^ 


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p 




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g 




^ 




g 


s 


fe 


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^ 








^ 


g 




^ 


1 




s 


g 


pd 


S=: 


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g 


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377 

1350 

1300 
1250 
1200 
1150 
1100 
1050 
1000 



= 950 



178 1.82 



1.66 190 194 1.98 

MOLLIER DIAGRAM <STEAM> 



2j02 



2D6 2J0 



Key 




EMTROPY 

See page 378 for explanation. 



378 



APPENDIX 



MOLLIER DIAGRAM— EXPLANATION 

Total heat of steam, H, is plotted against corresponding 
values of entropy. The condition of the steam as regards press- 
ure and quaUty are denoted by diagonal lines (see key, page 377). 
Any two of these diagonals intersect at a point which establishes 
the total heat and entropy corresponding to the condition. 

ExA]MPLE 1. Find the total heat of steam at 100 lbs. press- 
ure absolute, and a quality of 95 per cent. 

Fu'st, determine the intersection of the 100 lb. pressure line 
with the .95 quality line. At the intersection, read the ordinate 
value, 1142 B.t.u. 

Ex.\MPLE 2. Find the total heat of steam at 100 lbs. pressure, 
absolute, and a temperature of 378°. 

From the steam table, p. 372, it is found that the given tem- 
perature is 50° higher than the temperature of saturation at 100 
lbs. Referring to the ]\Iollier Diagram, find the intersection of 
the 100 lb. absolute line with the 50° superheat line. At this 
point read the ordinate value, 1215 B.t.u. 

Example 3. Find the condition of steam after it has ex- 
panded adiabatically from 100 lbs. absolute and 50° superheat to 
a final pressure of 15 lbs. absolute. 

The intersection of the 100 lb. line and the 50° superheat Une, 
on the chart, corresponds to an entropy of 1.636. Find where 
this entrop}' Hne intersects the 15 lb. curve. The corresponding 
quality is seen to be .916 and the total heat, 1070 B.t.u. 

Note that the difference between the initial and final heats, 
namely 1215—1070=145 B.t.u., is the heat available to do work 
on the Clausius cycle. This method is therefore useful to cal- 
culate the Clausius efficiency (see p. 235). 

Ex.^iPLE 4. Find the qualit}^ of steam from a throtthng 
calorimeter determination, data as on page 146. 

Take the calorimeter pressure as 15 lbs. and the absolute 
(high) steam pressure as 115 lbs. The superheat in the calorimeter 



APPENDIX 379 

chamber is 10°. Find the intersection of the 15 lb. Une, on the 
chart, with the 10° superheat hne. The corresponding total 
heat is 1157 B.t.u. Find where the 1157 total heat line inter- 
sects the 115 lb. line (tracing horizontally to the left). This inter- 
section represents the condition of the steam before expanding, 
and the quality, from the chart, is .961. 

Note. When scaling the diagram and tracing constant 
entropy or constant total heat lines, a pair of dividers will be 
found convenient. 



'^y^ 



380 



APPENDIX 



PROPERTIES OF AMMONIA 

(GooDENOUGH and AIosher) 





T> 


Specific Volume 


Heat C 


ontent 




Temp. 
Deg. Fahr. 


Pressure, 










Heat 


Lb. per Sq. 
In., Abs. 


of Liquid 

Cu. Ft. per 

Lb. 


of Sat. 
Vapor Cu. 
Ft. per Lb. 


of Liquid. 


of Sat. 
Vapor. 


of Vapor- 
ization. 


-40 


10.12 


0.0234 


25.45 


-75.3 


526.6 


601.9 


-35 


11.74 


0.0235 


22.14 


-70.2 


528.2 


598.3 


-30 


13.56 


0.0236 


19.35 


-65.0 


529.8 


594.7 


-25 


15.61 


0.0238 


16.95 


-59.8 


531.3 


591.1 


-20 


17.91 


0.0239 


14.89 


-54.6 


532.8 


587.4 


-15 


20.46 


0.0240 


13.15 


-49.4 


534.3 


583.6 


-10 


23.30 


0.0241 


11.63 


-44.2 


535.7 


579.9 


- 5 


26.46 


0.0242 


10.32 


-38.9 


537.1 


576.1 





29.95 


0.0244 


9.19 


-33.7 


538.5 


572.2 


5 


33.79 


0.0245 


8.20 


-28.4 


539.9 


568.3 


10 


38.02 


0.0246 


7.34 


-23.2 


541.2 


564.4 


15 


42.67 


0.0248 


6.583 


-17.9 


542.5 


560.4 


20 


47.75 


0.0249 


5.920 


-12.6 


543.7 


556 . 3 


25 


53.30 


0.0250 


5.336 


- 7.3 


545.0 


552.2 


30 


59.39 


0.0252 


4.820 


- 1.9 


546.2 


548.1 


35 


65.91 


0.0253 


4.364 


+ 3.5 


547.4 


543.9 


40 


73.03 


0.0255 


3.959 


8.9 


548.5 


539.7 


45 


80.75 


0.0256 


3.599 


14.3 


549.7 


535.3 


50 


89.09 


0.0258 


3.278 


19.8 


550.8 


531.0 


55 


98.03 


0.0259 


2.992 


25.3 


551.9 


526.5 


60 


107.7 


0.0261 


2.734 


30.9 


552.9 


522.0 


65 


118.1 


0.0263 


2.503 


36.5 


554.0 


517.5 


70 


129.2 


0.0264 


2.296 


42.1 


555.0 


512.8 


75 


141.1 


0.0266 


2.109 


47.8 . 


556.0 


508.1 


80 


153.9 


0.0268 


1.940 


53.6 


557.0 


503.4 


85 


167.4 


0.0270 


1.788 


59.4 


557.9 


498.5 


90 


181.8 


0.0271 


1.650 


65.3 


558.9 


493.5 


95 


197.3 


0.0273 


1.524 


71.3 


559.8 


488.5 


100 


213.8 


0.0275 


1.408 


77.3 


560.7 


483.4 


105 


231.2 


0.0277 


1 . 305 


83.4 


561.6 


478 . 2 


110 


249.6 


0.0280 


1.210 


89.6 


562.5 


472.9 


115 


269.2 


0.0282 


1.122 


95.9 


563.3 


467.4 


120 


289.9 


0.0284 


1.042 


102.2 


564.2 


461.9 


125 


311.6 


0.0286 


0.970 


108.7 


565.0 


456.3 



APPENDIX 381 



HYGROMETRY 

Hygrometry deals with the determination of the properties 
of mixtures of water vapor and air. Dalton's Law (p. 142) bears 
directly upon this subject and should be understood. 

It has been shown that a cubic foot of space at a given tempera- 
ture, tj can contain no more than a fixed amount of H2O vapor, 
regardless of the presence or absence of any other gas. This 
maximum amount is the weight of a cubic foot of saturated steam 
at the existing temperature, t. 

Supposing that the cubic foot of space contains air at the 
same time that it contains the maximum amount of H2O corre- 
sponding to the temperature, t. Then the air is said to be ^^ satu- 
rated,^' and to have 100 per cent relative humidity. If, however, 
there is less vapor than this present, 

Per cent, Relative Humidity 

__ Weight of water present, pounds per cubic foot ^^ 
Density of saturated steam at / degrees 

The relative humidity is determined by the " wet-and-dry 
bulb" thermometer, or '' psychrometer.'' This instrument con- 
sists of two thermometers, the bulb of one of which is kept wet 
by surrounding it with a wick saturated with water at room tem- 
perature. The evaporation from this wick lowers the tempera- 
ture of the wet bulb. The dryer is the room air, the lower is the 
wet bulb temperature; hence the difference between the indica- 
tions of the two thermometers is a measure of the humidity. The 
following table, taken from Kent's Mechanical Engineers' Pocket- 
book, may be used: 



382 



APPENDIX 















Relative Humidity 


f, Per Cent 






















Difference between the Dry and Wet Thermometers, Deg. F. 


Dry Ther- 
































1 


1 


1 


1 




1 


1 


n 


mometer, 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 13 


14115116117 


18 19|20|21|22|23|24|26|28j3C| 


Deg. F. 
































1 




1 


1 




1 


1 






Relative Humidity, Saturation being 100. (Barometer =30 ins.) 


32 


89 


79 


69 


59 


49 


39 


30 


20 


11 


2 




































40 


92 


83 


75 


68 


60 


52 


45 


37 


29 


23 


15 


7 

































50 


93 


87 


80 


74 


67 


61 


55 


49 


43 


38 


32 


27 


21 


16 


11 


5 

























60 


94 


89 


83 


78 


73 


68 


63 


58 


53 


48 


43 


39 


34 


30 


26 


21 


17 


13 


9 


5 


1 














70 


95 


90 


86 


81 


77 


72 


68 


64 


59 


55 


51 


48 


44 


40 


36 


33 


29 


25 


22 


19 


15 


12 


9 


6 








80 


9u 


91 


87 


83 


79 


75 


72 


68 


64 


61 


57 


54 


50 


47 


44 


41 


38 


35 


32 


29 


26 


23 


20 


18 


12 


7 




90 


96 


92 


89 


85 


81 


78 


74 


71 


68 


65 


61 


58 


55 


52 


49 


47 


44 


41 


39 


36 


34 


31 


29 


26 


22 


17 


13 


100 


96 


93 


89 


86 


83 


80 


77 


73 


70 


68 


65 


62 


59 


56 


54 


51 


49 


46 


44 


41 


39 


37 


35 


33 


28 


24 


21 


110 


97 


93 


90 


87 


84 


81 


78 


75 


73 


70 


67 


65 


62 


60 


57 


55 


52 


50 


48 


46 


44 


42 


40 


38 


34 


30 


26 


120 


97 


94 


91 


88 


85 


82 


80 


77 


74 


72 


69 


67 


65 


62 


60 


58 


55 


53 


51 


49 


47 


45 


43 


41 


38 


34 


31 


140 


97 


95 


92 


89 


87 


84 


82 


79 


77 


75 


73 


70 


68 


66 


64 


62 


60 


58 


56 


54 


53 


51 


49 


47 


44 


41 


38 



For example, if the wet bulb indicates 60° and the dry bulb 
70°, then the difference is 10° and the humidity is 55 per cent. 

Calculation of pressures and weights of air, water vapor, and 
mixture. The following notation will be used, all pressures in 
pounds per square inch absolute, and weights in pounds per cubic 
foot. 

Pmy T7m = pressure and weight of mixture; 
Pay TFa = partial pressure, and weight of the air; 
Pc, ir^^ partial pressure and weight of the vapor; 
Pj T^ ' = pressure and weight of saturated steam at tempera- 
ture, t; 
< = temperature, degrees F., of the mixture; 
//"^ relative humidity, per cent. 

To find partial pressures, given total pressure, temperature 
and humidity. Find P' from the steam tables, corresponding 
with t. 



Then 



P.-jqqXP', 



and 



■* a — -1 m -* r 



I 



APPENDIX 383 



The pressure of the mixture is to be found from the barometer, 
and the humidity as previously described. 

For example, if the barometer reads 29.33'', the corresponding 
Pm = 14: Al lbs. per square inch. Suppose the relative humidity 
is 55 per cent and the temperature of the mixture is 70°. From 
the steam tables (p. 370) saturated steam at 70° has a pressure of 
0.363 lbs. ( = P0- Hence, the partial pressure of the vapor in 
the mixture is 

P. = .55X0.363 = 0.2 lb., 

and 

Pa = 14.41 -.2 = 14.21 lbs. 

To find weights, given partial pressures, temperature and 
humidity. Find TF' (density) from steam tables corresponding 
to t. 

Then 

\\t 100^^^ ' 

144P 
^''' ^ 53.4 X (^+460) ' fr««^^^=«7^; 

For example, using the previous data, the density of saturated 
steam at 70° is 0.00115( = #''). 

PF„ = .55X.00115 = .00063; 

_ 144X14.21 
^"-53.4X530 =-0^25, 

TF„ = .00063 + .0725 = .0731. 



384 APPENDIX 



REPORTS OF EXGIXEERIXG TESTS 

A complete report should describe concisely the experimental 
object and how it was accomplished, and it should give numerical 
results and the conclusions formed from them. Whether the 
report is upon work perform.ed by a student in the laboratory, 
or by an engineer in practice, its material ma}^ be arranged to 
advantage under the following heads. 

(1) Object of the test. 

(2) Description and principles of apparatus tested. 

(3) Method of testing. 

(4) Sample calculations. 

(5) Results and curves. 

(6) Discussion. 

(7) Rough notes or condensed observations. 

The subjects under these sub-heads ma}^ be treated as follows. 

(1) Object of the Experiment. This should be a clear, 
complete, and concise statement, preferably in one sentence. 
Its purpose, in practice, is to enable the reader to decide without 
a full reading whether or not the contents of the report come 
within his scope of interest. In student work, it should be included 
as a matter of training. In any case, the object of the test should 
be stated in writing before its performance in order that the 
experimenter and others concerned shall have a clear view of 
the undertaking. 

(2) Description and Principles. This division should deal 
only with the machine, instrument, or apparatus tested. The 
extent of the treatment is governed by the requirements of 
those for whom the report is intended. A report prepared as a 
technical article or address kills itself if it talks over the heads 



APPENDIX 385 

of its audience or bores them with details with which they are 
familiar, however much satisfaction it may give the author. 
This is a matter for judgment. A good rule to follow is to 
give complete descriptions only of new or little known appa- 
ratus; for others it is sufficient to give only commercial sizes 
and names. It should be remembered, however, that any dis- 
tinctive feature or any characteristic affecting the test results 
should be fully described. This depends upon the object of the 
test. For example, in the report of a mechanical efficiency 
test of a steam engine, it is appropriate to describe thoroughly 
anything affecting friction in operation such as lubrication 
details, balancing of valves, etc. But if the same engine were 
tested for its steam distribution, lubrication need not be men- 
tioned at all; the valve mechanism then being the important item. 
In this division there may be deduced any formulas used in 
getting results provided they are original or unusual. Otherwise, 
they may be quoted without deduction, with reference to the 
authority. 

(3) Method of Testing. A logical way to begin this subject 
is by reference to the formulas for the quantities sought. Each 
formula, reduced to the desired form, shows the quantities that 
must be directly measured. The means of measuring them 
may then be described. Usual instruments may be merely 
mentioned by name, but special apparatus (original, or applicable 
only to the particular test) should be described fully. Any 
limitations of apparatus or unusual facilities affecting the pre- 
cision of measurements should be mentioned to enable the 
reader to judge for himself the accuracy of the results. For 
the same reason, the duration of the test should be stated with 
such items as frequency of readings. In this connection it is 
a good plan to refer to a sample set of observations which may 
be included in division 7. 

(4) Sample Calculations. In practice, these should some- 
times be included to make clear the method of testing and as a 



386 



APPENDIX 



voucher of the accuracy of the calculations. They should be 
omitted if these points do not need amplifying. They should be 
brief, proceeding at once from the expression for the desired 
quantity, in which is substituted the test data, to the numerical 
result. The form under Test 56 {d) may be used as a model. 
Reports by students should ahva^^s contain sample calcula- 
tions. The student should bear in mind that sample means 
something representative of the whole. Therefore, if five different 
quantities are tested for, three times for each one in the same 
way, five samples are necessary and sufficient. If these tests 
were repeated by another method involving a different calcula- 
tion, ten samples are needed. If only one determination is 
made of each quantity, the sample must be all of the calculations 
to be representative. 

(5) Results and Curves. Numerical results should always 
be presented in the form of curves w^hen possible, and also as a 
table. This enables the busy reader to size up the report with- 
out fully reading it. Curves and tables should have definite 
titles and enough information to explain their meaning without 
reference to the text. Curve sheets should bear the scales of 
coordinates, and the axes should be scaled for ready reading. 
Where several curves appear on one sheet, their plotted points 
should be differentiated by such conventions as circles in out- 
line, solid, half solid, etc. The points should be clearly marked 
so that they will not be obliterated when the curve is drawn in. 

The student should take care to differentiate between results 
and observations. Sometimes observations are results, but this 
is seldom the case. Further, there may be many intermediary 
quantities between the two which should not be confused with 
results. If the object of the experiment is clearly stated, it 
will always show what should comprise the results; in case of 
doubt, it should be referred to. 

(6) Discussion. This should deal with the probal^le accuracy 
of the results as affected by the precision of the instruments and 



APPENDIX 387 

methods used and as indicated by the concordance of the results; 
it should compare the results with corresponding ones from 
similar tests, records of which are available in hand-books or 
elsewhere; and it should give the conclusions to be formed relative 
to the performance of the apparatus tested and to the physical 
laws controlling the performance. The conclusions to be formed 
from a test are the most important part of experimentation, 
in fact, its very raison d^etre; so they should be fully given in the 
report. In practice, there w^ould be no value whatever to a 
test from which conclusions could not be, or were not, made. 

(7) Rough Notes, Observations. Complete reports should 
contain tables giving the observations in full so that their con- 
cordance and validity may be checked by the scientific investigator. 
When this is not considered necessary, a sample set may be sub- 
mitted, as for division 3. Students should include in reports 
the original notes taken in the laboratory, a loose-leaf note- 
book being used for convenience. 

Rough notes should be taken neatly and contain enough data 
not only to remind the experimenter of the noted quantities, 
but to enable an outsider without additional explanation to 
interpret them fully. Inexperienced observers, to save time, 
are prone to use arbitrary symbols or abbreviations in their 
notes, without meaning to anyone but themselves. The objec- 
tions to this practice are that the notes cannot be checked by 
others and the observer himself is apt to forget their meaning. 

In concluding the general subject of reports, it may be well 
to mention the custom of including in voluminous ones, as a 
sort of addendum, a synopsis of the whole work, relating briefly 
the results and conclusions. This enables the busy reader to 
get the gist of it without a full reading. In technical papers 
addressed to scientific societies, or published as pamphlets, 
such a synopsis should conclude the report. If published as 
an article in a technical journal, it should be at the commence- 
ment. 



388 APPENDIX 



A METHOD FOR CONDUCTING STUDENT TESTS* 

The following method has been used with success at Syracuse 
Universitj\ 

The first laboratory work assigned is, as far as the equipment 
will allow, individual. After a little training in the methods 
of the work, the experiments are given as problems, the theory 
of which is taught in the classroom. In the laboratory the 
student is quizzed at intervals during his work, to insure that 
it be performed not as a matter of rote. Approximate calcula- 
tions from observations are exacted as the observations are 
obtained. It is a great mistake to allow the postponement of 
such calculations until after the test is completed. This point 
cannot be too strongly emphasized. It is far better to have an 
experiment only partly but intelligently done than to have a 
vast amount of observations leading to faulty results and a half- 
grasp of the principles. 

As the course advances, the tests, especially those upon 
large units, require more than one student to make all the neces- 
sary operations and measurements. For the successful conduct] 
of some, it is expedient to have four or five stations at each ofj 
which one observer is needed. These advanced tests are imder- 
taken in this way. In the classroom the students solve problems 
upon the principles involved and are given the special instruc- 
tions which they could not reasonably be expected to obtain for 
themselves. When they have shown a satisfactory understand- 
ing of the principles, they are allowed to proceed with the exper- 
imental work, conducted as follows: For a test requiring five 

* Abstracted from a paper by the present WTiter on ** The Teaching of 
Experimental Engineering," Educational Review, June, 1912. 



APPENDIX 389 

stations, for instance, a squad of six men is selected. For the 
first fifteen minutes or so of the test, observers A and B are at 
station No. 1, C at No. 2, D at No. 3, E at No. 4, and F at No. 
5. Then B moves to station No. 2, where he is instructed by 
C in its duties. As soon as B has become famiUar with them, 
C moves on to station No. 3 and is instructed by D concerning 
the work there, after which D moves to station No. 4 with E, 
and so on. The scheme can best be understood by the follow- 
ing schedule. 



STATION 


NO 








Time 


1 


2 


3 


4 


5 


10 : 00- : 15 


AB 


C 


D 


E 


F 


: 15- : 20 


A 


BC 


D 


E 


F 


: 20- : 25 


A 


B 


CD 


E 


F 


: 25- : 30 


A 


B 


C 


DE 


F 


: 30- : 35 


A 


B 


C 


D 


EF 


: 35- : 40 


FA 


B 


C 


D 


E 


: 40- : 45 


F 


AB 


C 


D 


E 



Etc. 



The advantages of this method over shifting all the students 
at one time are obvious. There is absolutely no break in the 
accuracy of the observations or continuity of the test since only 
one man shifts at a time and he does not make measurements 
to be used before he has become somewhat familiar with the 
apparatus. The instructor is relieved of the small but essential 
details of instruction by the students themselves. Room is 
made for an additional man on the test without sacrificing the 
work of any of the others. A complete shift of every man can 
be made in a shorter time; in the example cited, the interval 
is thirty minutes. 

The time necessary for an observer at a station to instruct 
the newcomer varies, of course, with the duties of the station. 
In a boiler test the average time is about ten minutes, so that 
a complete shift of six men would be effected in sixty minutes. 



390 APPENDIX 

If all the men shifted at once, the interval should not be less 
than ninety minutes, preferably two hours. 

The shifting is automatic. All that each student needs to 
know is the sequence of stations, and to remember that he is 
to move to the next one only when he has been relieved by, and 
has instructed his successor. 

It has been found of considerable advantage to include a 
station the duty at which is to maintain a ^^ General Log.'' 
This contains the observations from all the stations. The student 
in charge of it checks to some extent these observations upon 
recording them, and is required also to calculate roughly indicative 
results as the test proceeds. The log may be used for reference 
by all the students and enables a clearer view of the whole test. 

At the end of a complete shift, three of the men are replaced 
by three new ones, and put upon the final calculations under 
the instructor's supervision. When these are completed the 
resulting quantities are plotted on a large chart, in common 
use for all who have made the test. In the meantime the test 
is continued by the three new and the thiee old observers, the 
arbitrarily varied quantity of the test having been changed. 
At the end of the next complete shift, half the .men are again 
replaced, the ones remaining being the more recent ones. In 
this way each group of three men serves two complete shifts 
and makes the calculations from the observations of one. 
When all the results are in, their concordance is checked by the 
regularity of the plotted curves, and these are presented as a 
whole to the class for consideration. 



INDEX 



ABSORPTION DYNAMOMETERS 

Absorption dynamometers, 34 
fan brakes, 38 

hydraulic friction brakes, 36 
Prony brakes, 34 
rope brakes, 35 
Accuracy, absolute, 1 
evidence of, 4, 7 
of instruments, 3 
Air, blowers, 336 (see also Fan Blowers). 
compression, isothermal, 344 
compressor efficiencies, definitions, 342 
compressor losses, 340 
compressor testing, 340 
capacity, 342 
efficiencies, 344 
heat measurements, 346 
indicator diagrams, 340, 343 
separation of losses, 345 
density, formula, 118 
head, equivalent to water, 116 
horse-power, definition, 336 
gross, definition, 341 
net, definition, 341 
measurement (see Gas Meters). 
required for combustion, 188 
steam mixtures, 383 
thermometer, 132 
velocity by anemometer, 124 
A.L.A.M. rating of auto engines, 301 
Ammonia, heat of the liauid, 333 

measurements, 318, 324, 327, 331 
tables, 380 
aqua, concentration test, 325 
heat of solution, 332 
heat of the liquid, 333 
specific gravity, 325 
compressor, indicating, 319 
pump test, 323 
Analyses of coals, table, 163 
Anemometer, calibration, 124 
correction factors, 125 
principles, 124 
Angular velocity measurement, 30 
Areas of circles, 368 
Ash in coal, test, 167 

A.S.M.E. standard of heat consumption, 229 
Atomic w^eights, 181 
Auto engine testing, 300 
economy, 302 
friction torque, 301 
mechanical efficiency, 301 



BRITISH THERMAL UNIT 

Auxiliaries of steam power plant, test, 247 

condenser tests, 276 

feed water heater, 281 
Avogadro's law, 181 



Barrel calorimeter, 152 
Baume scale of specific gravity, 359 
Belt dynamometers, 40 
friction, formula, 158 , 

test for, 159 
slip, allowance for, 337 

test of, 157 
tension, formula, 158 

test for, 160 
testers, 159 

constants of, 161 
transmission, efficiency test, 159 
Bilgram diagram, 213 

use in valve setting, 214, 217 
Blowers, 304 (see also Fa^i Blowers). 
Boiler, flue gases, excess air, 183 
horse-power, definition, 264 
leakage, heat lost to, 232, 249 

test of, 232 
performance, units expressing, 263 
test calculations, 270 
testing, coal measurements, 267 
efficiencies, 272, 275 
feed-water measurements, 268 
heat losses, 273 
sampling flue gas, 193 
starting and stopping, 265 
various results, 275 
Brake, constant, definition, 35 
fan, 38 

calibration, 38 
horse-power constant, 39 
Brakes, friction, 34 
constants, 35 
hydraulic, 36 
rope, 35 

unbalanced weight, test, 37 
Brake horse-power, definition, 35 

test, 224 
Brine, measurement, 316 
specific heat of, 317 
pump test, 323 
British standard of heat consumption, 228 

steam engine efficiency, 234 
British thermal unit, definition, 149 

391 



^ 



392 



DCDEX 



#1 

III 

HI 
ill 



CALORIFIC VALUE 

Calorific value, 170 [^s€t aho Heat Value). 
Calorimeters, 144, 172 {see also qualifying 

xcord). 
Calorimetric gas meter, 126 
radiauon correction, 127 
Calorimetr>- of steam, 139 
Carbon, in coal, esumation of, 168 
heat value of, 171 
dioxide recorders, 190 
monoxide, heat value of, 171 
Carburetors, adjustment, 286 
Carpenter's calorimeter, 148 
Central laboratory- dj-namometer, 45 
Centrifugal pump testing, 352 
capacity, 353 
eflficiencj-, 355 
horse-power supplied, 354 
independent variable, 353 
Chronograph, 31 
Circles, table of, 368 
Clausius cycle, .235 

eflBciency steam engine, 234, 378 
Cla\-ton's analvsis of indicator diagrams, 

" 208, 230 
Clearance of cylinder, testing for, 205 
by indicator, 208 
by mensuration, 206 
by water quantity, 206 
linear, definition, 205 
volumetric, definition, 205 
CO, analysis for, 195 

reagents for, 193 
CO*, analysis for, 195 
reagent for, 193 
significance of, 183 
Coal, air required for complete combustion, 
186 
calorimeters, 172 
carbon in, 168 
classification of, 162 

combustion of, 183 (see also Cotnbustion). 
commercial sizes, 164 
constituents of, 163 

heat value of, 171 {see also Heat Value). 
heat value calculation from analysis, 174 
heat value test, 173 
hydrogen in, 162, 168 
proximate analysis of, 163, 166 
sampling, 165 
ultimate analysis of, 163 
weighings for boiler test, 267 
Coefficient, excess, definition. 181 

effect upon products of combustion, 185 
formula for (coal). 201 
formula for (gas), 2Q4 
of friction, of belts, formula, 158 
definition. 156 
test for, 159 
variation of, 160 
of oils, test for, 156 
of performance, 314. 319 
Coefficients for nozilea. test, 107 
values of, 106 
for orifices for gas, 122 
for orifices for water, 119 



DENSITY OF A GAS 

Coefficients for weirs, 97 
Coffin planimeter, 84 
Combining discordant observarions, 5 
Combustible of coal, definition, 168 
Combustion, of coal, 183, 198 {see also Boiler 
Testing) . 
air supplied, 199 
effect of air upon, 183 
flue gases from, 185, 186 
incomplete, 183 
vapor formed by, 200 
complete theoreticaJ, definition, 188 

formula for air required, 188 
definition of, 179 

of fuel, calculations from exhaust gas, 
179 
predetermination of exhaust gas, 185 
of gas, 185. 201 (see also Gas Engine Test- 
ing) • 
air supplied, 203 

calculations from exhaust gas analysis, 
201 
incomplete, 200, 204 
of oU, 184 
products of, 180 
rate, definition, 264 
Complete theoretical combustion, definition, 

188 
Compound engine test, 236 
Condenser, leakage test of, 231 
•measurement of steam, 232 
surface test, 276 
jet test, 280 
Condensing calorimeter, 151 
formula, 151 
radiation correction, 153 
water equivalent, 150 
pyower plant, test, 246 
Constants for steam engine testing, 223 
Constituents of fuel, 162 

of oil fuel, proportions, 184 
Conventions for curves, 7 
Conversion of units of gaging, liquid, 116 
Cord, indicator, test, 60 
Corliss valve setting. 220 
Correction factor, definition, 93 
Corrections for steam turbine perfcnrance, 
246 
stem, 137 
Counter, continuous, 30 

hand. 30 
Couple, thermo-electric. 133 
Cur.ves. conventiors for plotting, 7 
Curve sheets, form of. 386 
Cvlinder clearance, 200 (see alf-y Clearance). 
Cvlinder condensation, 230, 233 
test, 233 



Dalton'slaw, 142 
D'Aubisson's efficiency of ram, 352 
Dead center of steam engine test, 211 
Density (see under required maieriaf) . 

of a gas, calculation from molecular 
weight, 197 



INDEX 



393 



DIAGRAM 

Diagram (see under qualifying word). 

factor, 242 
Discussion of test results, 387 
Draft gage, 27 {see also Gage). 
Drying steam, apparatus for, 147 
Drum motion of indicator, 57 {see also 
Indicator) . 
motion tester, Smallwood's, 61 

applied to reducing wheel tests, 74 
Duplex steam pump, test of valve motion, 

250 
Duration of time rate tests, 9 
Duty of pumps, definition, 257 

trials, 257 
Dynamometers, absorption, 34 {see also 
Brakes) . 
allowance for friction, etc., 44, 48, 49 
spring type, transmission, 46 
calibration, 48 
Central Laboratory, 46 
Flather, 47 
Van Winkle, 46 
weight-arm type, transmission, 40 
belt, 41, 44 
calibration, 43 
constants, 43 
pillow block, 41 
Webber, 42 



Efficiency, air compressor, 342 

auto engine, 300 

blower, 339 

boiler and furnace, 275 

boiler, grate and cleaning, 275 

boiler, overall, 272 

centrifugal pump, 352 

electric motor, 364 

gas engine, mechanical, 290 

gas engine, thermal, 295 

hoist, 356 

injector, 262 

producer, cold gas, 308 

producer, grate and cleaning, 312 

producer, hot gas, 312 

ram, 350 

refrigeration machine, 315 

steam engine, mechanical, 226 
thermal, 234 

steam pump, 252 

steam turbine, 244 

water turbine, 348 
Electric motor, test, 362 
Electrical horse-power, definition, 243 

output, measurements, 244 
Emerson dynamometer, 43 
Endurance tests of lubricants, 362 
Engine indicator, 50 {see also Indicator) . 
Equation, personal, 2 
Equivalent evaporation, calculation, 272 

definition, 264 
Errors, accidental, 2 

Error diagrams of indicator drum motion, 62 
from reducing wheels, 75 



FRICTION OF BELTS 

Errors of indicator diagrams, ordinates, 52 
abscissas, 59 
instrumental, 2 
Error, number of digits for 1 per cent of, 2 
Errors, personal, 2 
Error, starting and stopping, 9 
Evaporation, equivalent, 263, 271 
factor of, 263 
from and at 212°, 263 
unit of, 263 
Events of the stroke, measurement of, 218 
Excess coefficient, calculation of, 275, 299 
definition of, 181 
effect upon combustion, 185 
formulas, 201, 204 
Exhaust gas analysis, 189 
apparatus for, 189 
calculations from, 201, 272, 296 
reagents for, 193 
samphng for, 193, 291 
to be expected, formulas, 185 
from boiler, calculations, 273 
from different fuels, 185 
from gas engines, calculations, 296 
specific heat of, 273, 296 
vapor, heat contained by, 143 
variation with air excess, 185 



Factor of evaporation, calculation of, 271 

definition, 263 
Fahrenheit scale, 131 
Fan, brake, 38 {see also Brakes). 

blower testing, 336 

air horse-power, 339 

capacity, 338 

curves for, 336 

efl&ciency, 339 

horse-power supplied, 337 

independent variable, 336 
Feed water heater test, 281 

measurements, 268 

of steam, 231 
Fixed carbon in coal, test for, 167 
Flash point of lubricants, 359 
Flather dynamometer, 47 
Flow of air through orifice, formula, 122 

in pipes, test for average velocity, 117 

of steam through orifice, 128 
Flue gas analysis, 188 

apparatus for, 189 

calculations from, 198, 273 

reagents for, 193 

sampling for, 193 

to be expected, formulas, 185 
Flue gas, from dififerent fuels, 185 

heat losses, 273 

specific heat, 273 

vapor, heat contained, 143 

variation with air excess, 185 
Forces, measurement of, 12 
Francis' formula for weirs, 99 
Free air, definition, 336 
Friction of belts, formula, 158 
test, 160 



J 



3W 



INDEX 



FRICTION, COEFFICIENT OF 

Friction, coefficient of, 156 (see also Coeffici- 
ent). 
definition, etc., 154 
horse-power, definition, 223 

test, 226 
effect upon instruments, IS, 24, 43, 44, 49 
of indicator drum, test, 60 
of oil, test, 156, 360 
testers, 156 (see also Oil Testers) 
variation of, 155 
Fuel, constituents of, 162 

consumption of power plant, test, 246 
gas, 165 {see also Gas Fuels). 
oil, 164 (see also Oil Fuel). 
Fuels, theoretical reactions of, 183 (see also 
Combustion). 



Gage, draft, 28 

calibration, 28 

Kent's, 29 
hook, 96, 100 
pressure, 23 
calibration of, 23 

** test," 24 

testing apparatus, 24 
constants of, 25 
vacuum, 24 
Gaging liquid, conversion of units, 117 

specific gravity of, 28 
Gas, air required for combustion, 188 
analysis from assumed combustion, 185 
analysis, exhaust, 189 (see also Exhaust 
Gas Analysis). 
Gases, calculation of volume ratio, 182 

calculation of weight ratio, 182 
Gas combustion, 185 (see also Combustion) . 
Gas engine, advance of ignition, 283 

cycle, 282 

exhaust gas, effect of excess air, 185 

indicator diagrams, 282 

test calculations, 292 

test data, 293 
testing, adjustment, 282 

cylinder clearance, 205 

duration, 292 

eronomy, 290 

efficiency, mechanical, 288 

efficiency, thermal, 295 

excess coefficient, 299 

friction loss, 295 

fuel consumption, 292 

heat consumption, 294 

heat lost in exhaust, 296 

heat lost in incomplete combustion, 298 

heat lost to jacket water, 295 

heat lost to radiation, 298 

sampling gases, 193 

timing ignition, 285 

timing by indicator, 287 

timing valves, 284 

volume of exhaust gas, 296 

water vapor in exhaust, 297 
fuels, constituents of, 162 



HOIST. MECHANICAL ADVANTAGE 

Gas, fuels, heat value of, calculation of, lS5f 
294, 306 
definition, 170 
table, 171 
test, 178 
fuel mixture, adjustment of, 285 
fuel sampling, 178, 193, 291 
meters, 91 (see also under foUoiring), 
aneniometer, 124 
calorimetric, 125 
gasometer, 94 
orifice, 121 
pitot, 115 
venturi. 111 
volume, 93 
producer testing, 302 (see also Producer). 
standard cubic foot of, 171 
Gasoline, constituents of, 164, 300 

engine testing, 282, 300 (see Auto and Gas 

Engines). 
heat value of, 300 
specific gravity, 300 
Gasometer, 94 
Geared pump test, 356 
Goutal's formula for heat value, 177 



Xlead of air, equivalent of, 116 
Heat, balance, gas engine, 290 
gas producer, 302 
injector, 258 
refrigeration plant, 329 
steam boiler, 262 
steam power plant, 249 
consumed by a steam engine, 227 
consumption of power plant auxiliaries, 

249 
consumption of pumps, 256 
of steam in exhaust gas, 143 
of steam, measurement of, 141 
of steam mixed with perfect gases, 143 
of steam, notation for, 140 
unit, definition of, 139 
value, 170 

coal, calculation, 173 
coal, test, 172 
coals, table, 171 
definitions, 170 
elements, table, 171 
gases, calculation, 179, 294 
table, 171 
test, 179 

sampling for, 178, 193 
oils, 171 
test, 177 
Heater, feed-water, test, 281 
Heat transmission in condensers, 278, 280 
Higher heat value, definition, IVO 
calculation, 189 
test for, 178 
Hit-and-miss gas engines, sampling gases, 

291 
Hoist, test of, 356 
efficiency, 358 
mechanical advantage, 356 



INDEX 



395 



HOOK GAGE 

Hook gage, 98 

zero ot, test, 100 
Hooka's law, exceptions to, 19, 55 
Horse-power constant of brake, 38 

direct by planimeter, 84 
Humidity of air, 142, 381 
heat of, 143 
table, 382 
Hydraulic, friction brake, 36 
ram testing, 350 
capacity, 351 
efficiencies, 351 
independent variable, 351 
turbine testing, 347 

available horse-power, 248 
best operating speed, 349 
efficiency, 349 
independent variable, 348 
Hydrogen in coal by proxim.ate analysis, 168 
density of, 197 
heat value of, 170 
specific heat of, 309 
Hygrometry, 381 



Ice melting capacity, 314 
Ignition of gas engine, 283 
Illuminating gas, constituents, 165 

heat value, 171 (see also Heat Value). 
Incomplete combustion (see Combustion). 
Indicated horse-power, approximate for- 
mula, 224 
error from, 225 

direct by planimeter, 84, 226 

gas engine, 288 

steam engine, 224 

pumps, 253 
Indicator, applied to gas engine timing, 287 
cord, testing of, 60 

stresses in, 58 

stresses produced by redv.cirg wheels, 
68 
diagrams, abnormal valve setting, 215, 
287 

air compressor, 340 

air compressor analysis, 345 

Clayton's analysis of, 208, 220 

clearance from, 208 

Clausius cycle, 235 

combining, 239 

compound engine, 240 

correction of horizontal errors, 63 

correction of reducing wheel errors, 74 

correction of vertical errors, 55 

efTect of inertia upon, 52, 57, 68, 72 

errors of abscissas, 59 

errors of ordinates, 52 

error diagrams for, 62, 75 

errors from reducing wheels, 71 

factor, 242 

faulty, 217 

gas engine, 282 

logarithmic coordinates, 208,230 

mean height by polar planimeter, 76 

mean height by Coffin planimeter, 85 



LUBRICANTS, VISCOSITY 

Indicator, diagrams, sampling, 56 

steam consumption Irom, 229, 238 
steam engine, 51 
valve setting by, 215, 222, 287 
drum motion, errors of, 59, 71 
effect of guide pulleys, 62 
forces affecting, 57, 72 
drum motion tester, Smallwood's, 61 
drum motion, testing of, 61 
drum spring tension, adjustment, 59 

test, 59 
engine, 50 

reducing motions, 64 (see also Reducing), 
spring scale, test 53 
springs, calibration of, 52 

test apparatus, 54 

pencil motion, test, 53 

Injector, heat balance, 258 

test, 257 
Instruments, precision and accuracy, 3 
Intercoolers, effect upon air compressor 

performance, 340 
Internal combustion engines (see Auto and 

Gas Engines). 
Internal horse-power, steam turbine, 243 
Isothermal compression of air, 343 



J et condenser test, 280 
Junker calorimeter, 177 



Jvelvin's work scale of temperature, 132 
Kent's draft gage, 29 
Kerosene, constituents of, 164 

heat value of, 300 

specific gravity of, 300 
Kilowatt equivalent of horse-power, 243 



l^ap of slide-valve, measurement, 211 

of Corliss valve, 220 
Lead of slide-valve, measurement, 211 

of Corliss valve, 220 
Leakage, power plant, heat lost to, 249 
Leakage test, boiler and piping, 232 

condenser, 231 
Lcar^ squares, method of, 20 
Logarithmic coordinates, 208, 231 
Logarithms, calculations, 365 

tables, 366 
Logs for boiler testing, 268, 269 
Lost motion of duplex pump valves, 250 
Lower heat value, 170 

calculation, 179 

test, 179 
Lubricants, tests of, 358 

endurance, 361 

flash, burning and chill points, 360 

friction, 361 

specific gravity, 359 

viscosity, 360 



J 



396 



INDEX 



MAHLER'S CURVE 

Mahler's curve, 176 

formula for heat value, 175 
Manometer, conversion of readings, 23, 117 

mercury, 106 

water, 23 
Mean effective pressure, aggregate, 237 

correction of, 55, 63 

definition, 50 

equivalent, 238 

gasoline engine, 301 
Mean height of indicator diagrams, 76 

by Coffin planimeter, 85 

by polar planimeter, 76 
Mechanical advantage of hoist, 357 
Melting- and boiling-points, 137 
Meters, flow {see under Gas^ Steam and 

Water). 
Mercury, pressure equivalent of, 23 

specific gravity, 23 
Method of least squares, 20, 54 

of testing, reporting, 302 
Mixture of gas and steam, pressure of, 142 

for internal combustion engines, 285 
Moisture in coal, test of, 166 

in gas, test of, 310 
Molecular weights, 182 
Molecule-foot, definition, 181 
MoUier diagram, 376 

use of, 235 

explanation of, 378 
Motor, electric, test, 364 



Napierian logarithms, 365 

Ns, analysis for, 187 

Natural gas, constituents of, 165 

heat value of, 171 
Net air horse-power, definition, 341 

indicated horse-power, definition, 289 
Notation, boiler test, 266 

gas engine test, 293 

gas producer test, 305 

heat of steam, 139 
Nozzles, water, 104 

calibration, 106 

coefficient measurement, 107 

coefficient values, 105 

formula, 104 



O2, analysis for, 195 

reagents for, 193 
Object of tests, statement of, 301 
Oil, air required for combustion of, 188 

conibustion, 184 {see also Combustion). 

engine testing {see Auto and Gas Engines). 

fuel, constituents, 164, 183, 300 

heat value of, 171, 300 

heat value determination, 177 

lubricants, 358 {see also Lubricants). 

specific gravity, 300 

testers, constant of, 157 
types, 156 



PRODUCER, TESTING 

Optical indicator, 300 

Optical pyrometers, 135 

Orifice, flow of steam through, 128 

gas, calibration, 122 
coefficients, 122 

water, calibration, 120 
coefficients, 120 
Orsat apparatus, 189 

operation, 195 

reagents for, 193 

sampling for, 193 



x^antagraph reducing motions, 64 
Parr calorimeter, 172 

formula, 173 
Partial pressure of gases, 142, 276, 382 
Pendulum reducing motions, 65 
Pillow block dynamometer, 41 
Piping, leakage test of, 231 
Piston displacement, definition, 205 
Pitot gas meter, 1, 15 

best proportions, 116 

formulas, 117 
Pitot tube, traversing, 113 

water meter, 112 

mean velocity by, 115 
Planimeter, Coflfin, 85 
test of, 87 

on circular diagrams, 90 

polar, 76 

adjustment, 83 
equation, 77 
horse-power by, 84, 226 
testing, 83 
zero circle, 77 

radial, 88 
Platform scales, 13 

calibration, 14 

leverage ratio, 14 

sensitiveness, 14 

test of rider, 15 
Polar planimeter {see Planimeter), 
Power, measurements of, 33 

units of, 33 
Power plant, steam testing, 246 

pump test, 356 
Precision of instruments, 3 
Pressure, 22 

equivalents, 23 

mean effective {see also Mean), 

partial, of gases, 142, 276, 382 

standard, 171 

units of, 22 
Pressure gage, 23 

calibration, 25 

recording, 26 
Producer gas, constituents, 165 

density calculation, 307 

heat value, 177 

heat value calculation, 306 

specific heat of, 309 
Producer, heat balance of, 302 

test calculations, 305 

testing, 302 



INDEX 



397 



PRODUCER, TESTING 

Producer, testing, air supplied. 307 
capacity, 312 
efficiencies. 308, 312 
heat in cool gas, 308 
heat lost to refuse, 311 
heat lost to scrubber, 310 
heat lost to steam, 309 
necessary data, 305 
notation, 305 
radiation, 311 
sensible heat, 309 
starting and stopping, 303 
steam supplied, 308 
vaporizer water, 304 
volume of gas, 306 
weight of dry gas, 307 
Products of combustion, 180 
Properties, of ammonia, 380 
of steam, chart, 374 
explanation, 140 
Mollier diagram, 376 
tables, 371 
Prony brake, 34 (see also Brakes). 
Proximate analysis of coal, 166 
calculations from, 270, 305 
carbon estimation, 168 
heat value estimation, 175 
hydrogen estimation, 168 
sampling, 165 
table, 163 
Psychrometer, 381 
Pulsometer test. 262 
Pump slip, 253. 255 

Pump testing (see Steam and Centrifugal 
Pumps, Ammonia, Brine^ " Powers'* 
Injector, Pulsometer, Ram). 
Pyrometers, 135 
calibration, 136 



Vuality of steam, 142 
sampling for, 144 
tests for, 145, 149, 151 

R for air, value of, 143 
Radial planimeter, 16 

Radiation correction, calorimetric gas 
meter, 127 

condensing calorimeter, 147 

Parr calorimeter, 173 

separating calorimeter, 148 

throttling calorimeter, 149 
Rankine cycle, 233 
Rankine's efficiency of ram, 352 
Rating of auto engines, A.L.A.M., 301 
Ratio of expansion, 242 
Reactions of fuels, theoretical, 183 (see also 

Combustion) . 
Reagents for exhaust gas analysis, 193 
Recording instrument charts, 88 

averaging, 90 
Recording instruments, CO2 analyzer, 190 

flow meters, 101, 110, 127 

gages, 26 



STEAM CALORIMETERS, SAMPLING FOR 

Recording instruments, tachometers, 30 

thermoinetors, 133 

V-notch weir, 101 
Reducing motions, 64 

calibration of, 66 

errors of, 66 
Reducing wheels, 67 

effect of friction, 77 

errors produced by, 71 

force of acceleration of, 72 

forces in operation, 68 

testing, 73 
Refrigerating effect, 313 
Refrigeration plant tests, absorption, 321 

compression, 313 

heat balance, 329 
Reports of engineering tests, 301 
Riehle oil tester, 157 
Rope brakes, 36 (see also Brakes). 
Rules for testing, 8 



Sample calculations in reports, 303 
Sampling, box, 194 

coal, 165, 172 

exhaust gas, 190, 291 

fuel gas, 178, 193 

indicator diagrams, 56 

producer gas, 304 

steam, 144 
Separating calorimeter, 148 

calibration, 149 

radiation correction, 150 
Simmance-Abady CO2 recorder, 192 
Slide-valve setting, 210 

effects of adjustments, 210 

equal cut-offs, 213 

equal leads, 212 

by indicator, 215 

lead measurement, 211 
Slip of belts, 160 
Slip of pumps, definition, 253 
Specific gravity, Baum^ scale, 359 

conversion, to Beaum6 scale, 359 
Specific heat, flue gas, 273 

test for, 255 

of brine, 317 

gas engine exhaust, 296 

producer gas, 309 
Speed regulation of engines, 224 
Spring instruments, calibration, 18 
Spring scale, test for, 19 
Standard cubic foot of gas, 171 

pressure and temperature, 171 
Standards, primary and secondary, 3 
Standard thermometric scale, 133 

weight gage tester, 25 
Starting and stopping boiler tests, 265 

producer tests, 303 
Steam boiler testing, 262 (see also Boiler). 
Steam calorimeters, 144 
barrel, 152 
condensing, 151 

radiation corrections, 147, 150, 153 
sampling for, 144 



398 



INDEX 



STEAM CALORIMETERS, SEPARATING 

Steam calorimeters, separating, 148 
throttling, 145 
water equivalent, 152 
Steam, chart of properties, 374 
consumption, 227 
consumption tests, 227 

injector, 257 

power plant auxiliaries, 247 

pumps, 256 

refrigerating machines, 322, 335 

steam engine, 229, 237 

turbine, 244 
distribution in engine, 218 
Steam engine, constants, 224 

indicator diagrams, 51,215, 216, 240 
testing, cylinder clearance, 205 (see also 
Clearance). 

cylinder condensation, 234 

dead center, 211 

economy, 227 

efficiency, mechanical, 223 

efficiency, thermal, 234 
multiple expansion, 236 
valve setting, 210 (see also Slide-valve). 
Steam, from coal combustion, formula, 201 
from gas combustion, formula, 203 
heat content, 200 (see also Heat). 

definitions, 139 

notation, 140 

measurements, 141 
tables, 371 
meters, 127 

calibration, 130 

Curnon, 128 

General Electric Co., 128 

St. John, 129 

Venturi, 129 
power plant testing, 246 

auxilaries, 247 

engine, 247 

heat balance, 249 

leakage, 249 
properties, chart, 374 

tables, 371 

MoUier diagram, 376 
pump testing. 

capacity, 299 

duty, 257 

economy, 256 

efficiency, mechanical, 255 

efficiency, thermal, 257 

losses, 255 

slip, 255 

valve setting, 250 
quality tests, 145, 149, 151 
sampling, 144 
tables, 371 
turbine testing, 242 

corrections for pressure, etc., 245 

economy, 243 

horse-power output, 243 

internal horse-power, 243 

losses, 244 
valve laps, measurement, 211 
valves, 212 



VARIABLES, DEFINITIONS 

Stem corrections, thermometers, 137 
Student tests method of conducting, 388 
Suction diagram, gas engine, 289 
Sulphur, heat value of, 171 
Surface condenser test, 276 



Tachagraph, 31 

Tachometer, 30 

calibration, 30 

recording, caUbration, 33 
Temperature, definition, 131 

measurement, 131 

standard, 170 
Testing, rules for, 8 
Thermal unit, definition, 139 
Thermo-electric pyrometers, 133 
Thermometers, 131 

calibration, 133 

constant volume, 133 

electric resistance, 135 

gas, 132 

materials of, 131 

mercury-in-glass, 132 

recording, 133 

scales, 132 

stem corrections, 137 

wet-and-dry bulb, 381 
Thermometry, 131 
Thoma.s gas meter, 126 
Throttling calorimeter, 145 

formulas, 146 

radiation correction, 147 
Thurston oil tester, 157 
Timing gas engines, ignition, 285 

valves, 254 
Transmission dynamometers, 40, 46 (see 

also Dyyiamometers) . 
Trapezoidal weir formula, 99 
Traversing pitot tube, 113, 117 
Turbine (see Steam Hydraulic). 



Uehling CO2 recorder, 191 
Ultimate analysis, table, 163 

heat value from, 175 
Unbalanced weight of brake, 37 
Unit of evaporation, definition, 263 
U-tube, 23 (see also Manometer). 



Vacuum gage, 24, 277 
testing apparatus, 24 

Vacuums, ideal and actual, 277 

Valve motion of a duplex pump, 250 

setting (see Gas Engine Testing, Slide- 
valve and Corliss Setting, Steam Pump 
Testing). 

Van Winkle dynamometer, 45 

Vapor tension, 142 
tables, 370 

Variables, definitions, 6 ' 



INDEX 



399 



VELOCITY, ANGULAR 

Velocity, angular, 30 
of approach of weirs, 97 
head of air, 336 
measurement of gases, 111, 115, 121, 123, 

125 
of steam, 127, 149 
of water, 96, 104, 106, 112, 115 
Velocities in pipe section, 113 
Venturi, gas meter. 111 
calibration, 111 
water meter, 107 
calibration, 109 
coefficients, 108 
coefficients, text for, 109 
formula, 108 
recorder, 110 
Viscosity of lubricants, 358 

test, 360 
V-notch weir formula, 99 

recorder, 101 
Volatile matter, definition, 162 

test, 167 
Volume, gas meters, 93 
calibration, 95 
correction factors, 93 
measurement of gas, 93, 306 
of steam, 127 
of water, 92 
water meters, 91 
calibration, 92 
correction factors, 93 
Volumetric efficiency, air compressor, 342 

vrater equivalent of steam calorimeter, 152 
of Parr calorimeter, 173 



ZEUNER DIAGRAM 

Water, horse-power, definition, 252 
test, 253, 347, 353 
meters, nozzles, 104 
orifice, 119 
pitot, 112 
venturi, 107 
volume, 92 
weirs, 96 
pump testing, 347 (see Steam and Centri- 
fugal Pumps, Injector, Pulsometer, 
Hydraulic Ram). 
turbine testing, 347 (see under Hydraulic) , 
weight of, 23 
Webber dynamometer, 42 
Weights, measurement of, 12 

table of, 369 
Weir calibration, 100 
coefficients, 97 
test for, 100 
values of, 98, 99 
formulas, Francis', 98 
rational, 97 
trapezoidal, 99 
V-notch, 99 

velocity of approach, 97 
Willans' law, 232 
Work scale of temperature, 132 



i^ero circle of planimeter, 77 

equation, 77 

measurement of, 81 

of h(;ok gage, 100 
Zeuner diagram in valve setting, 218 



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